I want to build a solid top Roubo workbench, or something close to it anyway. In my neck of the woods for some reason nobody has good wood near me. I have the big box stores and literally all they have that's dried, aside from the overpriced hardwoods which would bankrupt me, is 2x4x8' studs. No 2x6 or anything slightly useful like that. There's some hardwood stores a couple hours away but they never have enough selection to go home with all my wood in one trip and I have no interest in or time to go back and forth. I live in Redwood country so there's plenty of that but it's so overpriced it's not even worth considering, not that it would be good for a bench anyway.

Now to my question:
How bad of an idea would it be to trim down those 2x4's to about 1" x 2.5" and use them stacked and laminated to get a ~5" thick top that's ~22" wide? Would the layering for thickness be a obvious no-no for some reason? I realize it'll be a crappy solution, and I'm okay with that as long as it's not something that'll tear itself apart.

Also, I was thinking of doing a short non-built-in set of drawers on the Roubo shelf with clearance under the top, which I could remove if it got in the way. Could the weight of this set of drawers make up for a thinner top, in the 3" range?

I'll take any and all help I can get. Thank you in advance.

- Kevin