Abrasive sheets should be attached to the surface plate using adhesive like 3M Super 77, not tape.
Unless you are using optical quality glass, the surface flatness is not as good as you think. Plus glass will bend/flex if not supported by a flat surface. A calibrated surface plate is preferred, but even lower grade plates can be pretty good. And they are usually pretty cheap for a small one, like 18" x 24" size.
Grinding compound will work both ways - on the aluminum and the grinding plate and the removal will be proportional to the material hardness. Best to use grinding compound for that final step - lapping part to part.
<<Would machining give more precise surfaces or just waste of time and money?>>
Machining (cutting) is for getting the surfaces to the right dimension and location (parallel, perpendicular, etc.)
Machining (grinding) is for getting a better surface finish on the machined surface.
Hand surfacing is to get a completely flat surface and to get a finer surface finish (remove all cutting marks).
Hand lapping is to match two surfaces regardless of their shape/finish.
Material removal for the above is greatest to least in the order shown.