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I second your opinion on mineral spirits... even just for cleaning pre-paint, it seems to leave a little bit of residue behind.
If you haven't already done so, you *really* should get those body mounts removed to clean under them. For example, one of mine had over an 1/8" of rust scale under it... then you could paint the whole frame at once. Replacing that rubber is definitely worth it as well. To remove, insert a punch from top of the mount and catch the lower part's lip (you'll see what I mean). Both halves are basically a washer with attached tube going into the rubber - the bottom one is just smaller and slip fits into the upper with a locking detent. Soak with penetrating oil (like PB) 1st. Energy Suspension makes a very nice poly set - just be sure to salvage all of the original metal as it gets re-used with most of the aftermarket sets.