After a week of planning and fearing the worst, I got my game plan together and successfully removed side rails with no noticeable cabinet damage.
Step One shows what the kind folks here suggested doing, and that was mask off underneath the rail. In fear that the tool would mar the cabinet, (Step Two) I inserted waxed playing cards on top of the tape and slid them under the rails as far as they would go and then taped them down. Step Three is pretty self explanatory. I started at the back and inserted the tool on an angle, and shimming it up to sever the tape and continued pushing up until it hit the bottom of the rail. I removed the tool on an outward angle to prevent it from touching the cabinet and washed, rinsed and repeated until it was done.
The first side took about 20 minutes and the second side took less than 10.
Installed the new rails this morning and I'm done...for now