I would think that commercial kitchen suppliers would have something big
enough; not likely to be cheap, but in my
experience not likely to be junk either. The only one that comes to mind locally is Russel Food Equipment.
Beyond that, 'commercial' stuck into your search string might help get pots of the appropriate scale.
I have a feeling there are liquidators for used restaurant equipment, but not specific knowledge thereof...
I think you're on the right track re: height and thick bottom. Might even experiment with a spacer below like a cast-iron grill or some such... especially if you can't find a very thick bottomed pot, or decide the added expense is prohibitive.
As far as the expense being worth it... I have regretted buying the cheap tool a lot more often than I have regretted buying the expensive one, regardless of what sort of tool it is! Really the only times I've regretted the expensive tool were when it wasn't the right tool, or a tool that I actually needed; it sounds like you're exercising due caution on that front.