Have you tried measuring the depth of the cut-out area and taking that value away from the depth of the body to give the actual wood depth at that point?

You may well find that you need to raise the pickup height up anyway, so you could glue some wood blocks to the bottom of the cut-out to give you the height, plus more depth for screws.

I'd prefer to fit some foam under the pickups rather than use springs, or even sit the pickups on the top of two or three short but wide brass wood screws, which you can use to adjust for the pickup height, then screw it down using screws through the tab holes so that the pickup is solidly attached to the guitar.