So how ya like the sticky mess of spraying an oil? Sucks right! Make it a point to learn water-based Topcoats, You'll be glad ya did.
Ummm, a word of caution, wait more than a couple days to rub an oil finish. 2 weeks or even longer. They take time to cure.
All goodly advice to which I would add the following:
Whereas your new toy is never going to be a high-performance plane and since you need to sharpen anyway, why not camber the iron and turn it into a fore plane?
Since you need to remove at least an 1/8" if not more to get past the rounded edges of the 2x4's and since you've just cambered your iron, start by traversing the board. i.e. Work directly across the grain for most of the grunt work.
Once you get close, start angling your strokes diagonally, getting closer and closer to planing the length of the board. Back off the depth of cut as you go. Eventually, you'll get it close enough that a random orbit sander can take it the rest of the way home.
Yes, construction lumber can be hand-planed to a shimmering surface. But if this is a glue-up of studs straight out of the clamps, you're not there yet.