Leveling any tile is hard, time consuming and can be expensive. And your tiles are HEAVILY textured...which means you will NOT have a flat surface. You will still see the straight lines where the grout used to be...because the textured of the tile will be disrupted by straight lines of "flat" cement. Even if you get this flat, you then have to sand the tiles to get rid of the shiny finish. Whew. Plenty of work. Painting it out afterwards then leaves it open to peeling and problems with the finish giving out after 5 years or so.

It would be sad to do all that work, pay all that money for materials only to have the paint FAIL after only a few years. If you want a solid surface in a single colour, you can have a high-end concrete counter top installed over top of the tile. It should cost 1.5 TIMES as much as removal and replacement with an entry level granite. But the tile will be 'left in place' which is your first criteria.

Personally I would bust it out (can be as little as a $1-$2/sf foot for labour) and then go over the plywood (the stuff the tile is sitting on) with laminate. It would look beautiful and last for 20+ years....and it would be cheaper than leveling tiles or over-laying it with concrete.

At 65 years old, you have another 20-35 years on this planet, and hopefully in this home. You can have a decent counter top without remortgaging your home. But the tiles need to go before anything of substance/value/longevity can be put in.

Ask yourself how disappointed/upset you would be if you levelled and painted these tiles only to have the finish fail in 5 years. If that is an upsetting thought, then you might want to look at removal and replacement with a nice laminate (some of them are GORGEOUS) that will serve you for the rest of your time in your home.