Home depot sells acrylic tile paint for like $50 a can.

These products are basically a tinted primer and in my opinion it's a better idea to use a good quality primer and good quality finish (I do not mean top of the line such a SW Duration or the Bullseye product you were looking at) but a 100% acrylic latex or a higher solids alkyd if you are painting exterior.

Probably some siliconized acrylic caulk like DAP Alex Plus, which, manufacturer's claims aside, simply does not take paint as well as regular acrylic caulk (DAP Alex).They probably figured it was worth taking the risk of you complaining about it.

But I did grab the 36" vanity for $50 as I picked up a random 36" top last year for $25.https://www.lowes.com/pd/Scott-Living-Robinson-Coffee-OAK-Single-Sink-Vanity-with-White-Acrylic-Top-Common-36-in-x-18-in/1000326503

The grout you use to do them with is acrylic,  self seals against staining, and is dry and ready for clean up within 1.5 to 3 hours depending on the brand.

You can get acrylic panels (about the size of a sheet of plywood and 1/4 - 3/8" thick) which have a high heat resistance - they were frequently used in engine rooms and galleys of boats and in fish plants when I was a kid.  

The vanities were in bad shape, so we have already bought some upgraded vanities with real marble* tops and new faucets, but not sure if we should also do a major remodel to replace the dated 1980's floor and wall tile, "Roman" whirlpool tub ("bone" colored), "bone" colored toilet, and acrylic shower stall.

From there you can either install an acrylic surround as some have suggested (less expensive, but cheaper looking), or you can install new backerboard/waterproofing/tile.You might have mechanical, plumbing, and/or electrical running above that drop ceiling.

Right now I am looking at Aker CM-60 fiberglass for around $420Aker ACCTS-3360 acrylic for around $800Delta 226032AL00 "Acrylic" $500 (although I've heard that it is just an acrylic layer over other material).Any suggestions of different units or recommendations of things I should be avoiding?

A high-end paint company may also deal in the 100% acrylic products that some companies use.