Don't paint the tile, man. That's really bad.
The existing tile is 7/16? The vinyl floor is floating and its about 1/8 to 3/16 thick. Flooring is always the issue, with different thicknesses through the house. Sound like stripping the floor is the way to go to get it flat by shimming the entire floor with the correct thickness throughout. One room at a time with this lil' guy
https://www.cpooutlets.com/factory-reconditioned-makita-hm0870c-r-11-lbs.-sds-max-demolition-hammer-with-case/mktrhm0870c-r.html?ref=pla&zmam=31282435&zmas=47&zmac=722&zmap=mktrhm0870c-r&gclid=Cj0KCQjwvb75BRD1ARIsAP6Lcqu-DRtQIiouLECrHbm9yLy9yeZL8iJO3Os0IrxmaigIYZYI9wab8c saArvjEALw_wcB
Save your arms, shoulders and upper body. No way around it, you have to do it on all 4s. Get something soft for your knee and get to it. It will take you a couple hours a day to do one room if you are a DIY. My guy will ding me about 2000 bucks to rid of all you described. They will get rid of it too. Sometimes, its not worth DIY. Maybe I am just getting lazy?