You can run a ULP that will place tRestrict circles around through-hole pads, which will prevent routing away from the pads on the top layer. Then there will be no need to solder these pads on the top side (where they are obstructed by parts).
I don't remember where this ULP is -- it might even be part of the ones that come with Eagle. Or you can just do it manually.
You can make manual vias by just inserting a wire into the via and soldering both layers, then trimming off the wire ends. I think LPKF actually sells some kind of rivets that you push in to the vias that can make this process a bit faster, but are likely to be expensive. Rather than worrying about vias like this, it might be easier to just forget about milling out the top layer and replacing all traces with wire jumpers that you solder in yourself. Clearly, you'd want to limit top-side routing in this case -- you can set the cost of top-side routing to be high in Eagle's autorouter (or route manually).
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The Ruggeduino: compatible with Arduino UNO, 24V operation, all I/O's fused and protected