You won't find 165 grain FMJ's. There are 168 grain HPBT match bullets, Not cheap stuff though. Lots of 150 grain FMJ's.
"...a single stage press isn't a good match for a semi-automatic rifle..." It's a technique thing. Been using one for eons, myself. Bin of lubed empties on one side of the press, empty bin on the other. Use one hand to put the case in the shell holder, operate the ram and pull the processed case out with the other hand while reaching for the next case. Do one operation to all your cases, then switch dies and do the next step. A powder thrower speeds up the charging. Not conducive for loading match quality ammo though.
Spending a rainy day getting the brass to the point it's ready for powder and storing them in some container(a shoe box or whatever you have.) saves time. Keep you out of trouble for one day at least.