Hey Petr,
I'm sure you remember my composite balsa sandwich build. I'm not sure that I would recommend a skim build with it. First, most skimmers want some mass associated with the board, when they go to do aerial rotations of the board, like during a big spin or a shuv, the mass helps the board rotate in place, otherwise there is a tendency for the board to go off to the side or some crazy place, while too heavy just makes those rotations like a 3 shuv almost impossible.
Also, most skimmers are pretty thin, as you noted - 3/4" to 1" inch is the usual range. The composite sandwhich gains it's strength component from the distance between the skins, you'll not really have any useable distance here. A lightweight 1 pound or less EPS, I would bet, will crush below the skins, if you try and thin that out such that WITH double 1/8" skin's combined with the EPS core net a total width of less than 1 inch. Plus, at that fairly thin amount, it's a bit of a challenge to bag a skin, the evacuation tends to seal off before your skin is fully bonded tight. You can bag like jan is showing with a fairly thick rocker bed and only vacuum forming the skin. Pay careful attention to how close the rail sides are to the table, that'll be inperative. That picture above looks like a skateboard deck. Those are something crazy like 9 ply and they aren't light. If you go above 2 pound EPS, you really don't need a skin, that's common surfboard density, so you're adding weight and complexity without gaining much.
Why not just bag some divinycell or corecell? Recently, 4 pound and lighter cores have been used - H-45 and Corecell comes in denisties from A300 thru A600 - 300 is 3# and 600 is 6# respectively.
Make your rockerbed or mold and then bag the straight sheet of high density foam to that. Balsa's density ranges from 6# to 12+ # so, very likely a solid layered balsa wood board would weigh more than a high density equivalent and also would not have the consistency from piece to piece as a HD foam - piecing together the balsa such that your board was balanced end to end and side to side would be quite the challenge.
I'd vote for corecell, A400, 3/4" thick, 1.5" nose rocker, no tail rocker or maybe minimal like 1/8". Simple build, consistent weight AND you can manage the weight going in, rathet than hunting for specific sticks of balsa. My two cents.
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