Probably not. That's a scary thing to build. Cobalt-60 gammas are hard to shield, and 2000K is really hot. The laws of physics don't forbid building such a thing, but I wouldn't want to be in the same building with it.
Okay, so you have something that's so self-heating that it'll easily melt rock. In fact, it's hot enough that it self-liquifies quickly at STP. Cobalt reacts weakly with oxygen, but you'll still have to be careful with it in air, so you'll have to seal it in something; at 2000K, there are only a few materials with which you can hold and seal it, tungsten being one. Also, it's radioactive, and the tungsten sphere you put it in isn't nearly sufficient to stop the gammas.
So, you get your tungsten sphere all ready to go, let the cobalt liquify itself, pour it into the sphere, and then lower/drop it into a borehole. Better not be any water down there, or it might come back up.
Once you've got it doing it's melting thing and it's really deep at the bottom of a borehole, it probably can't hurt anyone.
I can't imagine a funding agency being ballsy-enough to fund it, and _really_ can't imagine a nuclear regulatory agency being interested in letting you build a source that could get itself so thermally hot.
I spoke too-quickly regarding the radioactive shielding requirements, they're more manageable than I thought [1]. For the 10-cm thick tungsten wall, following [1], it looks like the shielding factor is ~25,000. That's more significant than it sounds, because only the gammas emitted at the surface of the cobalt see that shielding factor. The rest are better shielded, up to factors of 10^11 in the best case (propagating all the way across the sphere).
It's still a spooky thing to assemble, but it does appear that if the shielding is preserved, that it could be done without ridiculous quantities of assembly/launch shielding.
A 30cm sphere has a volume of around 1.1 x 10^5 cm^3. Cobalt's density is about 8.9g/cm^3, so we're looking at roughly 10^6 grams of 60Co, or about a ton of the stuff.
60Co puts out 1100 Curies of radiation per gram, so this sphere represents about 1.1 billion Curies. To put this in perspective, a nuclear weapon detonation releases on the order of 1-5 MCuries of fallout: the Chernobyl disaster vented about 200 MCuries into the environment: total contamination left behind by the Soviet nuclear weapons program is estimated at around 3 GCuries.
I am not sanguine about a research experiment that requires assembling multiple Chernobyl's worth of high level gamma emitters in a red-hot capsule, dropping it on the ground, and hoping it stays intact ...
I imagine the safe way of deploying the thing would be to assemble it on-site, over the bore hole, robotically. Don't have any humans anywhere near the entire operation as long as all of that cobalt is in the same place (deliver it to the site with several delivery missions, each only having a relatively safe amount of cobalt).
(Apparently the cobalt would be inserted into the tungsten sphere as a not-yet-liquid sphere. That would make the multiple deliveries and robotic assembly more difficult, so maybe a liquid-assembly like you suggest could be arranged.)
How the hell do you weld tungsten anyway? Maybe make the sphere in two halves, then spin them up in opposite directions and push them together, to friction weld them?
Interesting that you mention HHO as crackpot theory.
What I am familiar with are kits to generate HHO gas for hydrogen welding. Mainly, they rely on electrolysis of water and gathering of H2. Of course, the amateur kits have blowback preventers and other tech to prevent gas explosions.
But nothing crackpot. Guess I don't read the cranks documents.
I think the name "HHO" itself hints that some amount of bullshit is taking place - the electrolysis units are obviously burning a 2:1 mixture of H2 and O2, not some weird mixture of atomic hydrogen and oxygen or impossible isomer of water. Empirically (via youtube), there is a strong connection between "HHO" promoters and "water-fueled car" and "over-unity generator" fraudsters. Oxyhydrogen torches are pretty awesome - I've used both a small electrolysis unit for jewelry work, and a larger tank-fed torch for working with fused quartz. Amazingly clean and hot flame, with definite niche-applications. However, oxyhydrogen combustion (electrolysis-derived, or otherwise) isn't exactly a revolutionary technology. We've made industrial use of it since the 1860s [1], and the trend has been gradual replacement by other fuels and techniques (TIG, electric arc furnaces, etc) that are more controllable and lack H2's unique shortcomings - eg. hydrogen embrittlement, massive range of explosive concentrations, and incredible ability to diffuse through things.
[1] Faraday's 1861 lecture on platinum-group metals is a great example. Small-scale platinum casting is one of the big uses for oxyhydrogen - the combination of a high melting point and severe carbon embrittlement make H2 ideal for working with platinum.
Atomic hydrogen welding is basically taking a COTS plasma cutter and blowing H2 thru it and welding with it, not welding with H2 but with hydrogen ions. On a scale of hazardous welding technologies, its up there. Possibly the only thing I'd less enjoy doing by hand would be explosive welding or some of the thermite processes. Its not "is there going to be a fire" but "how much damage will the inevitable fire cause vs the cost of alternative fabrication"
On the bright side (oh the pun) during the welding its pretty efficient at preventing weld pool oxidation. On the bad side, if long term hydrogen embrittlement is an issue with the base metal, this is an interesting way to find out. Also you can get some gas porosity problems as the weld bubbles while cooling, exactly CO2 in soda water, although hydrogen is better than the noble gasses (like argon in a plasma cutter)
Burning homemade H2 in a modified acetylene torch like you're talking about is comparatively harmless with the exception that H2 can find leaks that acetylene can't find, although its not that much worse. Oh and the regulator is different because acetylene comes out of a coke bottle solution like CO2 out of soda, but hydrogen comes out of a tank like O2 so the pressures are a bit higher.
This allows you to transport the Co-60 taking advantage of square-cube law scaling. In summary its a zillion times easier to keep a million Co-60 ball bearings cool and frozen than one big sphere because of surface area.
If you're really bored you can do the thermodynamics calculations for how small a pellet has to be to remain cool enough to touch safely (well, other than the radioactivity) in still room temp air, etc. Or if you're willing to clamp the pellet to a 10 C/W transistor heatsink (that heatsink is about the size of a postage stamp, is if you figure on a hot day your skin can tolerate about 10C temp rise without getting a burn, than that means your pellet has to dump less than a watt or so, of course there's no rule you couldn't use a much better larger heatsink, or a modest cooling fan, or drop it in a barrel of water, etc)
The biggest problem you run into with this kind of stuff is thermal shock from expansion. You might be well advised to find some low coeff of expansion cobalt alloy rather than using the straight up stuff. A straight up sphere, would likely shatter if big enough and the exterior is frozen and the inside is very hot.
Okay, so you have something that's so self-heating that it'll easily melt rock. In fact, it's hot enough that it self-liquifies quickly at STP. Cobalt reacts weakly with oxygen, but you'll still have to be careful with it in air, so you'll have to seal it in something; at 2000K, there are only a few materials with which you can hold and seal it, tungsten being one. Also, it's radioactive, and the tungsten sphere you put it in isn't nearly sufficient to stop the gammas.
So, you get your tungsten sphere all ready to go, let the cobalt liquify itself, pour it into the sphere, and then lower/drop it into a borehole. Better not be any water down there, or it might come back up.
Once you've got it doing it's melting thing and it's really deep at the bottom of a borehole, it probably can't hurt anyone.
I can't imagine a funding agency being ballsy-enough to fund it, and _really_ can't imagine a nuclear regulatory agency being interested in letting you build a source that could get itself so thermally hot.
TL;DR -- lots could go wrong.