I have not tried it on melamine but I think it will work.  I use my 4-1/2” angle grinder with a flap sanding wheel.  It makes fast work of stock removal.  I use it regularly to scribe crown molding.

The direction of the grinding is downward and it does not chip out the finish on pre-finished moldings.  I believe it will do the same on melamine. 

There are videos on line on how to do this with crown moldings.  It takes a few practice cuts to get the hang of it.  For me, it was just on how to hold the grinder. 

Wear glasses.  There is stuff in the air full time.  And a mask is not a bad idea either.  If you can, do this outdoors.  It does kick up a lot of dust.

This is the type of flap wheel you need:

I'm soon to be installing some simple melamine shelves, two feet deep by about 8 feet long. I know the drywall isn't flat, so my plan is to cut the back perfectly straight, throw it up on the wall, and scribe with pencil along the back edge. Easy stuff.

But, knowing melamine is prone to chipout, what's the best way to make that undulating cut? I was thinking a compression spiral bit in a router, but visibility (following the line) is going to be tough. Belt sander would make a mess, and sadly it's the one sander style I don't own. Any other ideas?

If going the router method, perhaps get am 8ft length of 10mm thick plank. Scribe that and trim with a jigsaw or whatever. Then use the plant as a template, using a template profile cutter, or a following ring.

BOSCH T101BR jigsaw blades.

I assume these are the down cut blades.  I have one of those and they make very clean cuts on the top surface, but not so clean on the bottom. 

If you are using melamine from the big box stores you will have certainly have a harder time.  That stuff is notorious for its thin brittle coating.  Melamine from a cabinet material supplier is usually superior.

Jigsaw with down cutting blade as mentioned might be best choice.  If so, if possible experiment on a scrap to test how you saw reacts, speed setting, and oscillating setting if you have one.  I seem to recall that I didn't care for using the blades in my Carvex and that the best cut was with the oscillating off.

If your shelves were not to be adjustable, and the waviness was minor that you look at back beveling leaving a sharp point at the top and then doing the bump into the drywall.  That was a technique taught to me by a professional cabinet installer.

Peter

Power plane, this is what they're made for. Finish off with a swipe with a 180grit sanding block. I use the EHL65, due to dust extraction, ergonomics and, most importantly, the spiral blade. A 'must have' tool for installation work, but one that doesn't seem to get much attention in the Festool world.

The Thingamajig looks great. I'm going to snap one up, along with a cheap Power Planer. The HL 850 would be amazing, but not in my budget right now (and this is a tool I probably won't be using very often).

I tried a few different techniques to cut the scribe line. The angle grinder with flap disk worked fast, but caused tearout on one end of the melamine. Jigsaw was the worst, even with the Bosch T101BR blades. But it was fast.

Even though it was a little more time consuming, I made a template out of a thinner scrap piece, scribed and cut it with the jigsaw. Since it was a scrap template tear-out really didn't matter. To transfer the scribe, I cut most of the material away with the track saw (where I could) and then used a Rockler pattern flush trim bit to transfer the edge to the finished piece.

(The real reason I went through all these hoops - this was a big shelf, 10x2 feet, 3/4" melamine. Too large for me to install myself, and I didn't want my friend to have to sit around while we install it multiple times to scribe both edges since it sits in a corner. But the template was light enough for me to install and remove multiple times.)

I discovered compression bits really aren't necessary for hand routing melamine. A straight cutting bit is fine, but spirals will cause chip-out.