Tree of Heaven is worse still. I tried to clear a small property of it for a couple of seasons, and failed, so I unconsciously take note whenever I see it growing: it's seemingly everywhere.
Never dealt with those, but the worst for me was Brazilian peppertree. I had just one in my backyard and the best I could do over a decade was managing to keep it from spreading.
The most effective method was to hack into the bark to apply an herbicide, and give it a couple of weeks to make its way into the roots. Dig out as much as you can once the leaves all die. Good luck!
It's not much of a story - banana plants are ridiculously resilient; so long as it hasn't flowered yet, you can cut off the entire "trunk" and it will have started shooting the new leaves from the stump within a day.
This resilience applies to the part below ground too, and they're full of water, so it's a bit like trying to dig watermelons out of the ground, but if inevitably split one while digging, and you miss a bit it's just going to grow again, and if you take too long between bouts vs the plant (as with bamboo it's unlikely to be a 1-day affair for a reasonable size clump), some of the bits you cut will have broken down and started to rot, so the ground will be soggy and smell horrible.
