Some things to consider:
Steel Wool leaves tiny threads of steel in the wood, which can cause rusted spots in the wood. Especially aggravating when it's already under the finish.
A better alternative is Scotchbrite White pads which are equivalent to 4-0 Steel Wool. That is what I use on wood, and save the steel for metal work.
Scotchbrite is available in several grades, here is a chart of grit equivalents:
On BLO, I have used it on a few stocks with good results. Bear in mind though that it sinks deeply into the wood, so once it's in you will only be able to recoat with more BLO.
I think the original finish, if you can call it that, was a wipe-down with a BLO soaked rag, at least that's the way mine looks. Hardly anything there at all.
Tru-Oil is a mix of BLO along with other ingredients. This is from its MSDS sheet, available online:
If you are going to try and even out the finish using a stain, a gel type stain would be preferable, you can do small areas without a lot of bleed-out.