I suppose even a 1/4” layer of sound dampening membrane is better than nothing, but why on earth would replacement of the entire subfloor be required?  

***NOT taking off the old shingles, is only saving you around $1K (give or take)... if you're already going through all the hassle of new system, bite the bullet and do it correctly.When you remove the old layers, you can then: do any necessary repairs; possibly install ISO boards (insulation boards) smoothly; install the good membrane (not simple felt!)

Everything passed except for the "secondary roof" which consists of a membrane roof over an unheated, patio "room" separated from the man house by glass sliders.

Even in low end rentals, we only recommend 100% complete ceramic tile walk-in showers or cast iron/porcelain tubs with ceramic tile surrounds, and, depending on the property and the Owner preference, either a copper or membrane actual shower pan.

You will also want to use a decoupling membrane between the subfloor and the tile.  

Before tiling he would then roll-on a waterproofing membrane on the concrete board.

If you tile, you can put down a crack isolation membrane down under the thin set. 

The peel and stick membranes are rated for 30+ days of exposure and they have two layers.5) I have had roofing contractor quote me for GAF Timberline, Owens Corning Duration, and Atlas....

It's going to cost 1.5x or 2x what you projected.You will need waterproofing and basically build a "tub" of waterproofing membrane. 

Roof replacement shall include the removal of all existing layers of roof coverings down to the roof deck.Exception: Where the existing roof assembly includes an ice barrier membrane that is adhered to the roof deck, the existing ice barrier membrane shall be permitted to remain in place and covered with an additional layer of ice barrier membrane in accordance with Section 1507.1511.3.1 Roof recover.