Hi Randall,
Thanks for the reply!
Well Scott I'm afraid your going to be doing a tear out unless you have some mortar bed building skills.
No I do not.
What you have is the old fashion mortar bed walls. A rarity by todays standards. There aren't too many skilled pros who can even do that type of tile backer method.
Is that a better way to go? It sounds like HardiBacker and waterproofing is easier and is more in line with my skills.

That rusty bead has to go.
I noticed that the drywall had some issues prior to me starting this shower project. I'll have to cut the drywall out and fix that while I'm doing the shower. This is turning into more than I anticipated. It might be impossible for you to answer, but I know moisture caused the mildew/mold/rust problems...Was this a matter of the tile job, mortar bed, or caulking failure? The reason I'm asking is I want to avoid the same problem in the future.
At the point I'm at now, the shower doors had a good bead of sealant around it. The shower handle escutcheon was not sealed. The tub had silicon between the tub and tile. The escutcheon might explain the rust in the picture, but at the opposite end of the tub, I'm not sure. The lower 6" of the mortar bed was wet all around the tub.
I would suggest starting fresh. Rip everything out to the bare walls.
Are the existing painted walls drywall or plaster?
It's drywall. This is what I'm thinking of doing, but I'm open for suggestions.
Cut out the mortar bed.
Cut out the drywall back to the damaged sections.
Make sure the framing is all right.
Check plumbing for any leaks
Install HardiBacker Board
Waterproof with LATICRETE Hydro Ban
Install the travertine tiles with a 1/16" joint
Grout with non-sanded grout
Seal, suggestions on sealer?
Relax for about a week as my wife has more projects on line to which I'm not privy to. I'm on a need to know basis.

Thanks for your time,
Scott