I will be putting a 1x8 to the beam supporting the 2nd floor to match the beams I will be building
Are you wrapping the existing beam or just adding one 1x8? What are the dimensions of the original beam.
The code says 1.25" and you could sleeve it in conduit for protection. No boxes necessary, just make sure the cable doesn't get scuffed/pinched at the entrance/exit points.
I allow myself to make decisions sometimes. Although against code, if the cable was run along the very top of the beam, I can't see anyone nailing/screwing up there.