If "finicky" means you have tried 8 different pellets, domed that should / could shoot well, and none or just one does then maybe take a close look at the crown of those barrel.
No, it actually shoots most pellets well, but with a slightly more obvious preference for a couple, compared to my .22 rifles. But I think a couple of things may be in play here. My .22s are all well seasoned, and just luckily very accommodating barrels. My .177 Weihrauch is new, and I haven't had a really good calm day to do much testing. Not displeased with it at all.
Which model 177 Weihrauch are you shooting? If springer what is your scope/mount setup? They all have some generalized patterns of liking certain pellets.
It is the HW 100K, PCP carbine.
First thing did you knock the stock power level down to right around 18ftlbs? The HW100's all come setup shooting WAY WAY too fast for even the heaviest 177 pellets. Once you are under 900fps with heavy pellets you should notice a huge difference in accuracy on all pellets. Most people seem to find a sweet spot between 850fps and 890fps with some heavy 177. Your problem could be your tuned power level and not the pellets.
Once tuned down to that try the JSB 10.34, Crossman Premier 10.5 in milk carton or most anything around 10.5gr. If you like the lighter stuff for shorter range the JSB 8.44's are about the best but you can't blast them over 900fps either for more than 25yds. Once you get something like that dialed in good them play around with super heavy or the pellets with the goofy heads marketed to kill a rabbit deader than a Diablo.