I'll start this by saying there wasn't really anything wrong with the original fiberglass countertop. It was in good condition, easy to clean and not altogether unappealing. That being said, it lacked a lot in the structural department.
Apparently the construction method favored by Gardner Pacific, the long since defunct maker of the Sunrader, involved almost as much silicone adhesive as it did staples. The substance is indeed tenacious, but once it loses its grip it is completely useless. And in this case, the countertop had long since broken free of its original silicone attachment to the cabinetry. In addition, the builders used a number of plywood braces on the underside of the counter to make up for its rather limited stiffness. Around the stove in particular, strips of plywood acted as braces and provided purchase to the wood screws that held the stove in place.
During a previous removal of the stove I'd used some gorilla glue to reattach said braces, but it was only a temporary fix if that.
The bigger issue of the 'floating countertop' was really the lack of structural strength (integrity, really) of the cabinet itself. There really isn't much more to it than a particle board face frame and a few bits of 2x4 lumber to hold it up. Weight saving and cheap. And without the shear strength (no, not sheer strength) of the fiberglass counter to keep it square, the cabinet does an awkward version of the hula on the highway. Cue squeaky clattery noises. Ack.
Removing the counter is relatively easy. The stove comes out with just a few wood screws, the sink is held in by wing-nut tensioned clips, and the plumbing is all very straightforward. The only tricky bits are cutting (breaking) the fiberglass where it encircles the drain vent AND separating the support for the drawers from the underside of the counter. I used impatience whenever the utility blade couldn't quite make it through the luan. I know there are better techniques.
All the screws that had originally held the counter to the exterior wall had come loose, so it only took a little bit of coaxing for the last bit of silicone to release.
Fortunately, my source for custom counters came through in just a few days. With a little trimming using a router, the new top went in easily. I installed some 2x4 supports along the front of the cabinets (vertically) to provide some much needed rigidity and to provide a cleat for some wood screws up into the counter. The difference in structural strength for the cabinet is dramatic.
I got a new matching sink at the H-Depot and cutout the space for the stove after half a dozen more careful than usual measurements from the original counter. For the most part, everything went in quickly and easily. Next up is plumbing. I haven't worked with Pex before, but it looks simple enough.