Thanks for your post - and welcome to HN, we appreciate your posting here. On reflection I chose to delete the comment, unfortunately I saw that you wrote a reply to it afterward. I think my comment was overly critical.
I think the key insight that a lot of people may miss in your post is about timing - the first email your post quoted from Brian said they wanted to close $100K to operate "for the next 4 months", so a closing time 6 weeks later (1.5 months into that period) is quite late in that process. Early stage companies are radically underfunded and at times running on vapors. If you hadn't closed in time and the company had died, you never would have written about "the time you killed a $25 billion company* by not investing in time when you were the only investor who they could still count on". You would have long-since forgotten them.
So the lesson to investors is to cut the check! You may not have another opportunity.
Gather ye rosebuds while ye may,
Old Time is still a-flying;
And this same deal that smiles today
To-morrow will be dying.
You being up a great point around the potential of "killing" a great company and this is important. I was always sensitive to their position as I'd been there 5 years earlier when I bootstrapped my company.
I always negotiated in good faith with them and spent time to understand their needs. Look at the budgets: When you look at that budget with handwritten notes that's my writing - I was concerned they weren't raising enough and I asked them to take more money to get more runway AND i agree to increase the valuation to account for the dilution.
As far as the "six weeks goes" that was from the first day we met until the day I had my lawyers at Greenberg Traurig negotiate docs with their counsel at Fenwick. Part of the delay was my own stupidity; I had my lawyers drafting custom docs (which I paid for completely out of pocket and didn't push into the closing costs). Brian has rightly sent me standard YC docs to use but I was too ignorant to even know what those docs were. And then I spent two weeks negotiating terms and final valuation.
The other complication is Brian wanted me to meet with another angel he wanted to bring into the round (I left this out of the post as I didn't want to embarrass this angel; we actually became pretty right friends after all this). So this other guy and I met up a couple times before he decided he wouldn't do the deal and that delayed us as well.
But I was always direct on my commitment to Brian and once we agreed to terms I immediately had my lawyers move to closing quickly.
I just had a similar situation with a company we committed to fund this year. We were coleading the deal with another VC; this other VC ended up in a protracted (2 months) negotiation of docs. We (Arena) couldn't fund our half of the deal until docs were finalized with this other VC. So the founder calls me up because he's now 3 weeks away from missing payroll and may have to slow down user acq that's going great and He's obviously worried that if this seed round fails the company is dead. And I told him not to stress - I offered him a $250k personal loan to his company at the lowest simple interest rate and he didn't have to secure it or offer me any warrants or incentives. I peronsally funded his company two days later and we're all good.
My point being - I do understand the consequences of being a bad investor because I always try to imagine myself in the founders shoes. I was in that spot years ago and I know how vulnerable it can feel. Even though I wasn't a well educated investor when I was doing the Airbnb deal I never took any action that would have harmed their potential.
Six weeks for closing a seed/angel investment from introduction to term sheet sign-off is not "too long". From my reading, it seems there was a firm commitment on both sides and hence, it was bad of both airbnb and YC to cut you off totally. At the very least, I would have expected the likes of YC to allow you to co-invest instead of simply assuming you were a newbie marine. After all, it was not as if YC had seen some stellar exits by mid-2008.
I think the key insight that a lot of people may miss in your post is about timing - the first email your post quoted from Brian said they wanted to close $100K to operate "for the next 4 months", so a closing time 6 weeks later (1.5 months into that period) is quite late in that process. Early stage companies are radically underfunded and at times running on vapors. If you hadn't closed in time and the company had died, you never would have written about "the time you killed a $25 billion company* by not investing in time when you were the only investor who they could still count on". You would have long-since forgotten them.
So the lesson to investors is to cut the check! You may not have another opportunity.