Ideally when lapping you want the lap to be the softer material. This way the compound impregnates the lapp and cuts the material. A very simple flat lap can be made with 2 lengths of clear 2X4. sand them all flat on one surface with your glass. They are now very close to flat. Mark 1 edge 1 2 3 each on 1 board you want a #1 #2 and #3 board. with number 1 facing sand #2 and #3 facing then 1-3 with numbers apart and 2 to 3 with numbers apart The 2 to 3 numbers together and 1 to 3 numbers together. Put light pencil lines across working surfaces to see when they are cleaned up. Here a coarser paper 180 -220 is better as it cuts cleaner and faster and leaves a rougher surface to hold the compound. This will cut the steel quicker and truer. Even just off the glass it ight be good enough.
Most of the old cast iron and brass lapping plates had a line pattern in squares or diamonds cut in them to help hold compound and oil. These plates would cut fast and true When lapping on one a figure 8 pattern was used sliding from side to side and top to bottom utilizing as much of the plate as possible, this helped to keep the plate flat also.
with your makeshift wood plate use it right after dressing down so moisture changes don't affect it. Use an oil based compound and light oil to lubricate it. Last is rotate and use as much of the surface as you can working in the figure 8 pattern. Valve grinding compound is coarser than the "graded" versions and is expected to break down in use getting finer as its used
For a surface polish one of te clean blocks with flitz or toothpaste will really shine it up. Or rub some jewelers rouge in it