Interesting story. I have a neo flash cart and I've not had the problems you've described with ROMS at all. Maybe on a couple of occasions a game has frozen, but in 8 months of heavy playing that's hardly anything to write home about - normal PCE cards would do that.
I am convinced that the problem is with your region modded Duo-R. I recommend a standard PC Engine to use with the neo card, not the TG16, because I find that most of the US versions of ROMS are available in hacked versions which will work perfectly when uploaded onto the neo card and played in a Jap PCE. Not that you would need to play most of the US versions anyway, but it at least gives you the choice.
So yeah, I think it's the system you have - apparently neo test every card before sending it out, fully loading it and playing it, so I'm sure it isn't faulty.
I can help you out if you like, as long as it's not a problem with people on this board. I've could send you a ROM file that I know definitely works on my Neo Flash Card, and you could try it on your own. If it doesn't work, then it's not the ROMS that are to blame.