Quote - I think I understand this now: Genesis didn’t work (as I predicted).  All that texture stretching was a problem. 

This is incorrect. Genesis does work and because of how the mesh was designed it can create small and large meshes, adults and children. Different UVs are used for custom characters as well as being optimized for certain shapes; but texture stretching wasn't a major issue as you could interchange textures among the shapes. Genesis 1 is mostly used now for creatures and Genesis 2 is for male and female figures.

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With genesis 2, they went the opposite direction, and back to the M4/V4 unimesh concept (I’m not talking about the rigging) with a single mesh that they distort, and then provide different UV maps to us that compensate for the distortion.

This is incorrect as well.

Genesis 2 has a base female and male shape to have for gender-specific weight maps, rigging and allows content creators to make clothing for a gender-specific shapes such as bras and dresses, which were difficult to do because the base genesis character did not have breasts. Texture stretching was not a reason for Genesis 2. When you design a mesh properly, whether it's a figure or an outfit, you will not have major issues with texture stretching. 

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So M6 will take G2M morphs but not textures?

M6 is based on Genesis 2 male so morphs and textures (provided it has the supported UV) will work.

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Clothing use usually compatible (or fixable) right?

Clothing will fit figures for that generation: Genesis 1 clothing will morph to fit each figure (though there may be some stretching or clinging in the breast area), Genesis 2 will work with morphs from the respective base figure... So clothing for the G2F will fit V6, Olympia, Lilith, etc. The clothing will fit between the male and female using auto fit or using DAZ's Cross Figure tool. Genesis 1 clothing will fit Genesis 2 figures using Autofit as well.

NOTE: Autofit is a DS feature. For converted clothing to work in Poser, you would have to use DS to convert and save it, then create the companion files for it to work in Poser.  There are a few articles around that show how to do it, but if you don't want to use DS, then you have to settle for only new clothing. You will probably buy high heel shoes regardless because of how they convert. Flat shoes and boots generally convert better. Dress conversion may need one of Sickleyield's utility available at DAZ.

Some of the DS tutorials contain content that you can install and use as well.

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Olympia, Lilith, Victoria 6 are ALL different UV maps?  (what a mess)

What about Steph 6 and David 6, to they take V6 and M6 maps?

Yes, because you may buy or use only one figure and not the others. Also the UV is optimized for that character. Keep in mind these are considered separate characters, not morphs so they have individual UVs (and adjusted rigging), but the Genesis tech allows you to swap UVs between charcters or use UVs from previous generations (like V4 or F5, provided you have the UVs from add on products), so you can reuse what you have, though it will not be 100% compatible.

Quote -My real question is that textures: textures are going to be incompatible across all of these characters? Am I right?

No, see above.