What I've been doing is gluing the fretboard down then flush trim by hand then sand the radius. Good question about neck thru's, I haven't done one yet so I don't know what I would do.
As to the tape...3 layers is a lot in what way? Too thick or not cost effective? Just curious what you mean there. Ive also seen people use the masking tape but with super glue instead of 2sided tape. That might help if your thinking the 3 layers too thick.
Ah, if your fretboard isn't radiused yet, then you have more options. And if you already have a radius, you could probably stick some full-length shims on each side to get a flat, stable platform to run a router on, or to lay against a router table.
3 layers is a lot, compared to 1 layer, in terms of effort (3 times, in fact!). If I, for example, want to stick a template on top of a body to route for a pickup, putting masking tape on both surfaces in addition to double stick is more tedious than just using double stick directly on the wood. When using just one layer, the trick is, of course, learning how much double stick tape is needed to hold things steady, without using so much tape that things are hard to pull apart afterwards.
Nothing too bad about using 3-layers, but I do a lot of double sticking in one project, so it adds up! In terms of thickness or cost, the difference is negligible.