I brought it to GEICO for an estimate. They recommended trying to get it cleaned up at my local body shop and, if the paint got into the clear and needed to be repainted, they would let me take it somewhere I really trust (eclipsis, detailers domain, or detailing dynamics).
Fortunately, they were able to take it all out! They claimed it had not penetrated the clear and they were able to "buff it out" (?). I was just happy to have it look good-as-new for $550.
For future reference, was this the right move? It's leased and I'm hoping to upgrade to an M5 (or better, if that exists), so I wasn't as concerned about long-term (>3 years) effects.
Thanks everyone for all your help and support!