Marty's idea works for sure but we all stumble onto different ways to skin a cat.
I found an odd Craftsman wrench set that someone "gifted" me with was ideal. These wrenches have an odd open end side that works somewhat like a ratchet wrench. This end of the wrench has somewhat of a "hook" on it, it looks something similar to a Iine wrench or crows foot. I believe I used a 14mm size of this type of wrench (maybe 13mm)
Using the hook to grab the underside lip of the molding, laying a paint stir stick along the molding for protection, I could work the edge loose, inch by inch and as you progress, taking longer bites to as much as 6 inch progressions.