I have average knowledge of rhino, but would just like to point out that Boolean is rather for volumes, and not surfaces. So, the tools you need will definitely be in the Surface tools section. That said, ironically, the tool you need is CurveBoolean…
I opened your file, created two new layers. SelAll, then Dupborder. Then I did CurveBoolean, selecting a few curves at a time, locking the resulting curves before CurveBoolean the next batch. Eventually, I unlocked the three locked curves, and did a final CurveBoolean. First click outside the surfaces, then inside the “holes”.
Then Srf from Planar Curves, and it’s done. I’ve attached the result.
It takes about one minute to do, though much longer to explain!