Yes, the majority of Bullpups have a mushy trigger because of the linkage that connects the trigger with the sear. It's usually a rod that is the connection point. But on some cheaper bullpup kits out there it's a metal wire.
My PS90 has a mushy trigger but it's still a good shooting weapon.
As of right now the current platforms that can be used by lefties and normal folks without a problem is the FN P90, FN FN2000, and the Kel-tec RFB. The P90 ejects it's spent cases downward, the FN2000 and the RFB efect the spent cases through a small tube just above the muzzle of the firearm.
The AUG platform can be configured for lefties. But it's not a on the fly kinda thing. You have to remove the bolt and charging handle, replace the efection port cover, etc.....
The three rifles that I know for a fact that are right handed only are the FAMAS, SA-80/L-85, and Norinco QBZ-95. Possibly the SAR-21 from Singapore but I'm not 100% sure.
I'm kinda the same way but I am slowly leaning towards them..... A longer barrel in a smaller platform works for me. Hence why I got the PS90. After my Form 1 is approved it's going to have a 10.3 inch barrel with a overall length of 20 inches. That's a tiny platform plus it has a fifty round capacity. As of right now the PS90 with it's 16 inch barrel and overall length of 26 inches is the same size as a H&K MP-5 with it's stock extended.
The PS90 might be the only bullpup I'll ever own though.... no other one on the market has such a fast magazine exchange. Yea, training can get me to work a AUG just as well.... but I think my load out is now M4 Carbines for when things get nasty and a PS90 for regular conceal carry.