Losing coolant after overheating

If you see no external leaks and the carpet up under the dash near the heater is not wet then likely you have a blown head gasket(s). The 3.4 does not like getting hot, they tend to warp the heads when they do.
To see if that is the issue you could pull the spark plugs and use a wrench to turn the engine over and see if coolant comes out of the plug holes. If it does you need at least head gaskets and the heads machined. However, at it has high miles it may be cheaper overall to put a used engine in it (or if it is in very good shape with no other issues you might consider a re-manufactured engine) more money than used but the better ones like Jasper come with a good warranty and hold up well.

Good luck. We will be here waiting for an update.