I do AV and hang TVs for a living. You don't have to 100% of the time hit a stud if its 100% necessary a TV go somewhere.

If your mount fits over the studs and just doesn't have a hole, make one! Just drill a hole in the mount. If you have "The frame" TV mount this may not be an option as those mounts are tiny.

EZ Anchors and other high quality drywall anchors can provide over 75 lbs of holding force per anchor so in theory with 4 anchors you can hold 300 lbs. Obvisously that is not likely going to work in the real world but your TVs are under 100 lbs and spread across different parts of the drywall you will be ok.

If you are using "The frame" TV those are meant to be ON THE WALL so we get then right on the wall, we use in-wall boxes for video and electrical and a 3/4 furring strip as others have suggested you will have a 3/4 gap on the wall.

Another thing you can do if you don't care about drywall damage, and I have done this as well, is to cut open a section of drywall behind the TV and add your own stud! You can drill into the stud and it will use a large section of the drywall as a form of a washer so your holding power should be greatly increased. The larger the stud the better and if you are lucky you can anchor the new horizontal stud to the regular stud.

In the end though no one is likely ripping this down off of the wall in a way that is going to cause it to fail. But use the anchors appropriately and use the biggest ones! The EZ Anchors come in 50lb and 75lb sizes. Butterfly bolts or toggle bolts are good too I like the 1/4 size as the fit nicely in the holes of TV mounts a majority of the time.