While WD-40 is supposed to be great for cleaning off the bugs from the chrome/paint on the front of your rig prior to a wash down, spray them a few hours before to loosen them up...
But...back to the stains...my favorite de-greaser is "Dawn" dishwashing soap which I use on wooden handled tools to remove years of greasy filth to cleaning just about anything including wood that has any kind of finish (or none) prior to some BLO application for shovels and wooden handles that aren't painted.
I'm thinking you can whip up a pretty strong mixture in a bowl and with a sponge, get those stains off in a jiffy. Just don't let the soap dry on there, clean a little, rinse it off, clean some more, repeat...
Grab a Scotchguard sponge like the one the wife uses to do dishes and use the "rough" side.