I'm not a stock finishing expert. The poly does not penetrate deep into the wood. It mostly stays on the surface. The BLO is supposed to penetrate some,the finish being more IN the wood.
And there is an order to things.
You are right,staining on top f the BLO might not work so well.
I'm suggesting here. This might work.Give it a light sanding.
You might wipe it with turpentine or acetone or mineral spirits.
There is a process called "Whiskering" Wiping with a moist sponge will cause the grain to raise.With sharp,fine sandpaper lightly cut the whiskers off.
IMO,you will be way ahead to order some stock wood filler from Brownells.
Its function is to fill the pores in the wood.You will put a lot of time,dry time,nd work into just using BLO to get a fill. Some of the fillers are stained.
You can get your color from a stained filler.Follow the directions.Once thoroughly dry,lightly sand and you should see your wood grain.
You'll rub in small amounts of BLO,then give it cure time. A week might be good.Don't leave liquid BLO on the surface or you will get a gummy mess.
You are working a finish into the wood,more than on the wood.
Folks debate over whether the old BLO finish is a good way to go,these days.
But on some guns,its "right"