Is this loan being modified through the government's Making Home Affordable plan?
Based on what you have quoted about being on a partial payment plan, there is a reasonable likelihood that your loan will be reported to the credit reporting agencies as "paying under a partial or modified payment agreement". For others, this has resulted in drastic drops in score of 100 points or more. Since your scores are already quite high, you could possibly experience a drop of at least this much.
The other option you mentioned - deed-in-lieu of foreclosure - would also drastically affect your credit score, probably much worse than the notation that would come with your loan modification. It may drop your score just as much as a foreclosure. Like foreclosure, a deed-in-lieu would prevent you from obtaining a new conventional mortgage for as much as four years. If you have a second loan on your home, a deed-in-lieu may be much harder to negotiate.