Regarding flattening the plane sole, thicker plate glass scrap from a glass shop (at least 3/8" thick, preferrably 1/2"), and about twice as long, or so, as your plane, will provide a surface flat enough for the purpose. As well, with the popularity of stone kitchen countertops (at least in my area), it's easy to find stone countertop fab shops who have tons of scrap, often free (or cheap if they're really money grubbers) for the asking. I stopped at a local fab shop and he showed me the pallet of scraps that are refuse. Several kitchen sink cutouts, so around 30'ish x 18'ish inches. Heavy. Sharp edges that should be mellowed at home (same with glass). And for any woodworker's purposes, plenty flat. Stick a 3" wide strip of J-weight cloth 60-grit sandpaper to it, and you'll flatten the bottom. Follow up with 100 and 150 or so grits, and also relieve sharp edges on the plane bed that may develop. I also keep my shop vac with brush head handy, to clean the surface of the sandpaper as I'm working.
Years from now, when I can build my larger retirement workshop, I'll build a dedicated bench with one of these stone scraps as the top. It also works great as a flat surface reference for building flat board projects, like checking glued-up boxes for wobbling on 2 corners, so I know where to plane the high spots off.
Paul Sellers has his "oil rag in a can" trick for oiling plane soles, saw blades, etc., or a swipe of paraffin wax from a canning wax block (grocery store), these will help those tools glide along the wood in use.
