Hello Bill,
If you plan to be here for a long while then I'd first consider lifting the house to correct the sagging floors and possible enhance the foundation. If that's not a possibility, then my next approach would be to cut out the existing subfloor, improve the structure with additional joists while also re-leveling the room, and then replace the subfloor with two layers of plywood laid perpendicular to each other.
The third approach would be to pour a self-leveling compound to correct the level of the room, but this does nothing to improve the structure of the floor and might still allow for failure down the road.
Fourth option is an uncoupling membrane like Schluter's DITRA, but that's like pulling a cruise ship with a length of rope. "Might work? Might not be enough? Won't know until it snaps."
With the issues you've described, I wouldn't suggest that you use standard cement board.
Whichever course you decide upon, getting the dirt basement sealed up with plastic sheeting is probably going to improve the life, comfort and health of your home.
Best of luck,
Shaughnn

Shaughnn's right. In fact, I have exactly the very same issues with my 102 year old farmhouse, and it's the biggest reason my kitchen floor still hasn't been tiled. You can tell the time of year by the slope of the floor-- it actually changes slightly from season to season, and before I can do anything with it, I need to stabilize that movement, because it's way too extreme for ANY membrane. Your bathroom floors will probably be okay, only because they're alot smaller than the kitchen floor. But I'm assuming the kitchen floor covers quite a bit of area? In other words, more space to feel that movement to a greater degree?

Your best bet, before you start doing any kind of permanent finishes (even painting the walls, because the fix could end up showing cracks in the walls) is get a structural engineer in there to take a look and see exactly what's happening, and what needs to be done to correct it. THEN you can start thinking about remodeling.

it it easy to hold the house up while you dig a complete new foundation and full basement.
Insulated outside and underneath.
"... I'm on board with complete overkill and some extra expense if it is a permanent solution..."

Thanks for the comments so far.

I'm not a structural engineer, but I'm 99% sure I know why the floor is sloped. The house used to have a 2 story back porch, but somewhere along the line it got closed in and converted to a kitchen below and bathroom above. They just framed around the outside and sided. The floor still slopes backward away from the main building. It isn't like it is going up and down an inch with the seasons. It was just purposely built with a slope.

So, I guess my question is what method of leveling the floor (if any) will help minimize any seasonal expansion/contraction? Sistering additional boards to the joists to level and then new plywood? What thicknesses?

After it's level, is a membrane the way to go? Does adding 1/4" cement board under a membrane provide additional protection or is it just a waste since the membrane will move above it?

As for sizes, yes the kitchen is significantly larger than the bathrooms. It also has an attached pantry/laundry room that we would like to carry the tile through. That is why the potential movement has me a bit concerned. It has gotten a lot more stable since I regraded around the foundation and extended the downspouts out farther from the house. I will be putting plastic down (after I get all the junk out of there.) Still, a dirt basement is always going to have humidity swings.