I have done a little of lapping. Pretty much everything else really has failed one way or other but cast iron lapping plate, lapping paste and cast iron/steel has worked fine.
I would use any abrassive (sanding paper) on surface plate only if I had nothing else or nothing else would do.
Glass looks fine, but it is not really flat enenough to metrology. For normal fitting use you need many offcuts, most of them are not that straigh over length of 100 mm. Float glass is always wavy and slanted. Waviness seem to differ from piece to piece. But generally to one direction and 100-200 wave length on 10-12 mm glass I have measured. Also many glasses seem to be slanted, last piece I checked was about 0,1 mm tapered at distance near 400 distance. However, if you use figure of eight and randomize, the part will be more flat than the plate. Only caveat it that the glass ust be suported well ot the part must be light weight. Glass is pretty bendy.
Choosing the abrassive is interesting. I like the diamond when it is rolled into the lap and lap must be accurate like internal lap. Downside of the diamond is that it cuts forever. Loose lap is hard to clean out completely. Silicon carbide paste breaks down and it is very easily available 80/220 grit as a valve laping paste. It wears down fast, which is good and bad. Good thing when it braks dow the same pace as the part gets soother and smoother.
It really pretty much depends how accurate you need to go and are willing to go.
There is actually a learning curve, first thing to learn is that if the part is high and you push it. leading edge will wear down faster. Pretty nice when you try square something and it is just a little slanted. Second thing is to learn how to clean up everything. Third thing to learn is that you need more than one plate...to keep all the plates straight.
I need to straighten one worn granite surface plate. The granite quality is really good but the surface is not straight. Planning to use my lapping plate to straighten new brake rotor disc, check the straighthness of the rotor with another suface plate, then charge rotor with a diamond paste and use it to straighten worn surface plate. Few kinks that I need to verify prior to start.
Pekka