I'm in a similar situation. I purchased DLH Premium via the Chrome store in June of this year and would like to use this capability in FireFox as well. I'm hoping (and assuming) that it's not fair to charge a full second license just to enable a different browser, and that it's possible to get a valid cross platform license.
UNFORTUNATELY, at this point, I am getting 0% value from my existing Chrome license is. Prior to the last major update, VDH worked like a CHAMP and I absolutely loved your product. BUT, since the last update was pushed out, VDH Premium will only ever give me 4-5 options @ 674 bytes plus one webm file, but never a solid file... so I've reluctantly had to start using other download applications just to download ANY file.
WHY did I bring this up? Because I wanted to see if there was a difference between using this app on Chrome vs. FF so that I'd be able to value my "investment" in DLH Premium a bit higher.... than the current 0% success rate. :-)