I'm currently building a small switching layout and I've basically done what you've suggested, I have a large sheath of 6mm plywood covering the foam base. Should make it a little easier to install the switch machines.
I'll just have to do my best to drill a straight hole down from the top of the foam to the plywood base, about 2 inches. I thought I might be able to use the drill press to get a straight down hole but it won't reach the switches close to the middle of the layout. I suppose I could make some sort of wooden jig to hold the drill and have a guide to help it drill straight down??
Yes, attaching wood underneath the foam solves some problems and then creates others
Depending on the size of the hole you want, there are various options; the main issue is making sure the hole in the foam is clear if there is mechanical movement through it. You can use something like a knitting needle to punch through the foam and then drill out the ply with a sufficiently long drill, or you can use the drill by hand. My hand drill has a level bubble on the end so I use that to keep the drill bit vertical, but a drill press would work well (in fact, probably better). I mostly use a 3/16" drill (4.7mm) as that's the first drill bit that's normally long enough to get through with a stock length.
Alternatively for things like feeders, longer thinner drills are available online quite inexpensively; search for long 1/8" (3mm) drill or go to any good tool shop (at least here in the US), or if you can plan ahead enough, precut spaces in the underlying ply.
Another solution for smaller holds on top (e.g. under a turnout throw rod), I file or cut down the roadbed and slip a (pre-painted!) thin piece of styrene with the desired small hole under the ties, over the larger hole.
That aside, let me join in congratulating you on such a professional and useful video. It's easily as good as anything that's currently behind a paywall, such as MR Video Plus or Trainmasters on MRH.
One question I had is mixing the grout and and soil 50:50. Is that something you tried and it just works, or do you prefer the properties of the soil (for texture / colour etc) over plaster? Reason I ask is that there's very little light tan dirt where I live (it's all nice and brown or black) which has been an obstacle in getting nice scorched Australian scenery for me