SteveH ~ Welcome to the Corvette Action Center Community ~
This may sound a bit strange, but, you might try some brake cleaner. It works wonders on stuff like this. Spray the grease area and use a cloth to soak the grease spot. Re-apply as needed. The brake cleaner evaporates fast but cleans grease really good, esp. if you use a good absorbent type rag with it.
The only thing about brake cleaner is that it is terribly strong stuff. I don't know for sure, but it may ruin the color of your seat belts. It might also contribute to dry rot. Pay a visit to the junkyard first and pull a few seatbelts from there. Then you can experiment with different cleaners on those seatbelts that are already worthless.
Best degreaser on the market that is not solvent based. Approved for use by FAA for cleaning jet engines. Like 409 on steroids! Use sparingly as it is really concentrated. Brush into fabric and rinse with clean water. Easy! Will not harm color or fabric. The area cleaned will be clean....so, then you will need the rest of the belts.
I have to agree with Simple Green. BTW, this stuff works very well for cleaning anything from greasy parts to oily garage floors to the black streaks on the side of your RV from the rubberized roof . . .