It will take more than cutting the trim, you will probably wind up cutting out the bottom shelf of the cabinet.

There is no good way. Best fix would be to raise that cabinet 3" or more since you still need some clearance for air flow.

If you have no other option, the only saw that will make the necessary cuts---the front and front to back to remove the shelf cannot be done well with one type of saw.

A reciprocating saw would do all the cuts, but there is not much way to make straight cuts with a recip. saw. That type of saw is more for demolition than finish cutting.

If I were doing it and couldn't raise the cabinet (the easiest thing to do), I'd take the cabinet apart and shorten it by 2-3 inches. Depending on how the door is put together that would be more or less of a PITA. Steam and gentle persuasion should eventually work, though it might be easier to saw it off and re-make the bottom rail.

There's no way to notch it that will look good. If you have to do it I'd take the face frame off the cabinet and rip it on a table saw.

A Festool track saw will easily make chip-free cabinet grade cuts without removing the cabinet. You asked for the best method, not the least expensive:

Here is a link that might be useful: Festool

If all you want to do is remove the rope trim and the bottom portion of the bottom rail, the easiest way? I'd use a multi-tool. With care and a new blade, you can get a clean and straight cut.

That's going to be fugly! Have you already checked that the fridge feet are screwed as low as they will go?
Even if, IF you don't hit the bottom shelf, you will undermine its supporting member to a fatal degree.
If I came in and did this kind of job, you would be reporting me to the kitchen forum as a savage workman and they would be encouraging you to take me to court.
The only workmanlike (work-person-like?) way to do this is to take out the cabinet and modify it, and if there is enough room to raise the doors another 1", then, that; if no room, then you will need new doors made. And at that stage it's really cheaper to order a shorter cabinet _entire_.
Casey

I wouldn't use a multi tool. I can't imagine getting a cabinet grade cut with it.

The cabinet bottom may be compromised, but blocking between the bottom and side would easily fix that.