H320/H340 players work with both H100 LCD and H300 LCD remotes as well as with the non-LCD remote under Rockbox. There used to be a problem once with the key maps of the H300 LCD remote, but that has been fixed now (2 years+ ago...). So the page you've read seems to be quite outdated.
I have used all the remotes with my H340 and personally prefer the H300 LCD one. Happy bidding!
