They are not identical. Just because you cant understand the difference, does not mean that they are the same. I don't mean that in a rude way, its just not logical what you are saying. The same top width (3/4") belts are used on the 340 and 20 series, but that's about where the identical part ends.
Also, if you exceed the hp rating for the torque converter all bets are off. I cant tell you that it will or will not work, but most people run into premature wear of the drive clutch weights, and almost all have premature belt wear. You can try to avoid some of the problems by gearing for a lower speed so it puts less strain on the belt, but premature wear is unavoidable once you exceed the hp rating.
I don't think you will have a problem with heat, and you can adjust only a few things on the torque converters (on the driven unit mostly), but you don't need to adjust anything on them really. The 340 series is more tuneable i guess, but again, there is no real benefit to tuning it unless you are doing some drag racing or something like that.
That being said, i personally will be running a torque converter on a mini bike with a hopped up Briggs 5 hp engine and I'm making sure its the genuine comet one (id go with the 30 series personally because it give you better all around performance compared to the 20 series).
With that said, the 340 isnt that common, but you can check out the differences by looking at the drive ratio, etc from the manuals (340 series has a great overall ratio-but id still not go with it because its just pretty much very rare to see one)
340 manual
http://gtcmanufacturing.com/Comet-340-Series-OEM-Manual.pdf
and if you look around, the 20 series is the same as the 30, but 30 is assymetric, with assymetric sheaves and a different engagement/overall ratio. looking at the questions you may have, scroll down to the faq on mfg supply page.
http://www.mfgsupply.com/gomini/gominiclutch/gominiclutchtorq.html