29 years of experience eh .... that's a long time to be wrong.
Your floor must be ONE complete system from the joists to your tile.
We have a section on the main page regarding wire lath and scratchcoat. That system isn't meant for floors ... it's meant only for walls.
The 3/8" underlayment should come up with the vinyl.
If you counter-sink a circular-saw so that it cuts ONLY through the vinyl and underlayment, then cut the whole area you want to remove in strips of about 2 feet wide .... everything should peel up.
Test 1 strip about 12" wide first to make sure it's relatively easy ... then maybe make the strips a little wider.
Anyone who is in the business of offering customer support for ceramic tile and stone installations should be required to read at least ONCE the Terrazzo Tile and Marble Association of Canada (TTMAC) or Tile Council of America (TCA) handbook.
You need to determine the amount of bounce in your floor. You've got good joists with a close spacing so you should be fine, but THAT will depend on the longest unsupported span of the joists. Let us know and we'll help you make some choices.
