At the last roving marks I shot - 50lb longbow - I used POC shafts barrel tapered 5/16 - 11/32 - 5/16, with 63 grain steel piles. I used 2.5” parabolic fletching cut down to about a half of their original height, still with a parabolic profile. I’m afraid I cant remember what their all-up weight was, but it was less than 400 grains. From a quick longbow (Boyton, ash backed yew) I was getting past 220 yards with good arrow flight. I did some bare shaft experiments to get good flight over shorter distances first, and once I had a shaft taper/nock/pile combo that flew well, I copied it for the other 11 shafts. A little time spent experimenting and testing really does benefit in the end. Good luck.
2 1/2" Parabolics should be good. bear in mind for flight arrows I use 1.25"x 0.3" so that gives some idea how small you can go whilst still achieving stability.
I'd have though 100gn pile would be enough, and 5/16" shaft (in the stiffest spine you can get) would help if you want more distance.
All down to trial and error really.