I'm curious to see how this thread plays out, never heard anything like what you're describing before.
When you said the two loose valves feel "springy", I assumed that to mean you can compress the valve stem fairly easily, is that correct?? As bdalameda said, it is possible to compress the stem, but it takes a fair amount of force. You can force a feeler gauge that is slightly too thick into the measuring gap, and it will compress the valve slightly to accommodate the feeler gauge, but you'll feel a distinct 'snap' when you pull it back out. The fact that you said you didn't even hit bottom at .090" is extremely odd, and suggests you could easily stuff thicker and thicker gauges into the gap without much spring resistance. Can you be more specific regarding the amount of force required to push the valve stem down while taking the measurements.
Regarding your question about a broken valve spring being an easy fix, we don't know if that's even the problem for now, but how comfortable are you with removing the cylinder head? If you remove the head yourself and take it to a machine shop, its not generally an expensive proposition to do minor valve work.
And as Terry said, the typical shim thicknesses are in the range of say 1.80-2.20mm, so if someone forgot a shim entirely it might explain the clearance you're seeing in the .060-.090" range, but I recall the shims sit in a little pocket that takes up some (maybe as much as 1/4-1/2) of the shim thickness, so I can't imagine what's going on with your measurements to get that large a clearance.