I am surprised the Meguiars did not help since I believe it contains a petroleum distillate. That will usually cut through grease based dirt.
A couple of cheap things to try would be lighter fluid/charcoal lighter/kerosene/diesel oil (whichever you have handy). Or, if that does not sound like something you want to try, go to a Dollar Tree store and buy their de-greaser for $1.
If it is somehow minerals or chemicals from the rain, try a little vinegar.
You could also try a Meguiar polishing compound. I saw a guy mix equal parts of Meguiar's cleaning wax and polishing compound that he applied with an ordinary (not high speed) buffing wheel. It did a heck of a job in one step.
Just some thoughts off the top of my head.
Let us know what finally does the trick.