First of all, you still haven't specified whether your floor is "not flat" or "not level." Whatever else you have (or have not) done to get where you are, it would help a lot if you could say whether your problem is level or flat. Also, just to be sure here, if I am understanding you correctly, you installed the 2x4s ACROSS the 2x6s that make up the underside of the house? (Notice the very very NON-technical terms...so be aware that I'm not a builder or knowledgeable in this stuff like some of these people that post here...just sympathetic to rising note of panic in your posts....) The only reason I'm trying to clarify that is because I am wondering whether you installed the 2x4s "upright" (so the "4" dimension is vertical) or "laying down". I'm not trying to pile on to what you have *already* done, but I don't know what the proper distance for SPANNING that 2x4s have, and I don't know whether they can span two full feet if they are flat. This makes a difference because you want to install tile. If your subfloor is bouncy or bends ("deflects" I think is it), then all the tile you install will just crack and plague you and your heirs until the end of time...until you rip the whole floor and subfloor out again and re-do it. Or put in linoleum. Whichever comes first. You say in the top post that the cracks are like 1/4", but in your last post you write that they are up to 1". That's a big difference? Which is it? Does it vary from 1/4"-1"? Have you actually measure or are just eyeballing or going from memory? IF YOUR CRACKS ARE VERY SMALL: IF it were me (and it isn't), I'd probably just put down a very tight layer of Wedi board (thinset and screws/washers), seal the seams so it can hold the next layer, then put down a thin layer of self-leveling compound (though you still haven't said whether your floor is wavy or slanted), and then tile. IF YOUR CRACKS ARE 3/4'-1": Maybe use a layer of plywood (which would be cheaper but harder to cut), maybe tape and thinset the seams (ask someone on this board about this because I'm just brainstorming here), then use the SLC, then the tile. Only plywood will actually help form a floor (which I think you need to do with 1" gaps), not backerboard of any kind. Instead of Wedi, you could use probably any backer board (ask someone here what to do for the seams). But I only know about Wedi because that is what we went with, and I like it because it is light weight (good if you are a female working alone). I don't think your solution is in one step. It feels like you are going to have to create a tight subfloor, THEN level or flatten. I think you have a non-standard thing going on there, and that might not be addressed so easily with just one step before tile. One more thing, just out of curiousity, WHY do you think your floor must be level? Oh yeah, and I would start making your peace with a threshold. Given how non-standard your set-up is, AND the fact that this is DIY (or at least the subfloor), I'm not sure it is realistic to think you can get away with no threshold.

Hardibacker is not waterproof nor is it a good underlayment for vinyl tile or sheet flooring. The bbest water proof flooring will be sheet vinyl. There are no seams or grout lines. Sheet vinyl(and tiles) need a smooth surface on the underlayment. You can do that fairly inexpensively by installing cheap 3/4" thick ply on the joists. Then add a layer of rosin paper or 15 pound builders felt(roofing underlayment) That layer eliminates any squeaks from plywood rubbing against plywood. Then install a good grade of AC plywood with the finely sanded side up. Use a seam filler to fill the seams and apply the vinyl flooring adhesive directly on the plywood and then the sheet flooring. Sheet flooring can be tricky to install as a first time DIY project, so having pro's do that part might be best. If you do want to try it yourself, use heavy brown paper to make a template of the entire floor, lay that over the sheet vinyl and cut. Be careful not to tear the vinyl as it is installed on the floor--dry fitting it---NO adhesive. Once the vinyl fits, fold back an area, apply adhesive, and roll the vimyl back over the fresh adhesive. Then do more of the same until all the vinyl is adhered. You will need a 100 or 200 pound flooring roller(rental mplaces have them) to rollm the entire floor to securely affix the vinyl to the adhesive.

"....above a garage." Says it all. I would guess the structure isn't ready for something heavy like tile or stone or concrete. The effort to get those products in there = 1-2 inch FLOOR RAISE to get the stiffness + the stone on top. That is a BIG toe stubber. Vinyl = man made PVC (polyvinyl chloride). All man made from the 40's (ish) Lino = natural products going on 150 years (linseed oil, cork, jute, wood dust, etc) Cork flooring is VASTLY different from crumbly cork boards (used at a desk to hold things to the wall). Cork glue down tiles are 4mm - 12mm thick and can last 100 years or more. In fact there are Cathedrals and churches in Portugal and Spain that have their cork floors for more than 100 years. The US Library of Congress received their cork flooring in the 1890's (just before they reopened at their 2nd/current location). It's still there. And cork is water proof. That's why the wine industry uses cork....because it keeps the liquid in the bottle. The bottles of Champagne found on the Titanic (yep...the stuff brought up to the surface once it had been found) were still 'sweet'. Which is to say NO salt water had entered the bottles despite the crushing depths.

The travertine I looked at looks like a gold or yellow tone. I continued searching for vinyl tiles, and I am now overwhelmed. The ONLY flooring place near us (1/2 hr away) was the one who suggested Coretec Pro Plus. She picked the colors with my oak wood. Originally she picked a medium dark brown vinyl plank. I thought that vinyl planks next to real wood planks (a cabinet) was a huge no-no. Maybe it was for a vinyl wood floor next to a real floor that was a no-no. The medium oak color is going to have to stay since he installed it today. He had already stained and finished it. Reading hundreds of Houzz posts about vinyl tiles/planks has not helped. Footprints, cloudy floors, scratches...oh my! Some people hate vinyl and others love it. They even have the exact same brand. I found one post with over 2200 responses. I will read it tomorrow. I can't find any color that I like except for the wood looking planks, but I think the tile looking vinyl would look better. I am out of time. I paid for the baseboard trim to be installed, but now we will have to install it ourselves. The contractor is almost finished so I will have to pay him with the trim uninstalled. Not his fault I couldn't find what I wanted. I just don't know what to choose. He told me ceramic tile was out which was what I wanted originally. I discovered Supercore today, so more research is needed. I am so sick of remodeling.