I've also used SoftSoap in a pinch. It works quite nicely. But yes, I forgot that one time when I had got the Dawn out to bathe my mat, I accidentally used it on the marker marks. Sorry to hear you had so much trouble with the Ultra Cleans. I just LOVE them. I have even left the red marker on for 4 days once & it still came out no problem. Dyed the bath water all pink & freaked me out, but sure enough, it all came out with the 2nd rinse.
I have switched to the UltraClean crayons for some things, though. They only come in fat tip, I think, but they usually come out with just plain water & a white rag. I just wet the rag a bit & rub for about 30 seconds & most of it comes out. The rest will just brush off once it dries. The nice thing about the crayons is that there's no risk of getting marker down into the batting. I have ironed over both the markers & the crayons and they still come out. Can't really beat that for functionality -- iron, sew, quilt, apply heat, use steam & leave on for days.
The only thing I can't say for sure if it's okay is how the markers react with sizing or starch. I pre-wash all my fabrics & don't starch them once they're marked. Hopefully you won't have those kind of problems ever again. So glad you got it out of your quilt.