You might want to also talk to Atlantic Training Support as they offer a Citation 550 initial rating, which would be done on an aircraft.
Aircraft Type and Type Rating Courses | Atlantic Training Support
Not heard of anyone offering an abbreviated course to go from C525 to C550. I know Bristol Flying Centre / Centreline can do it the other way round (as you say) if you have enough jet experience (I seem to remember it was 500 hours)
ND