Get a piece of plywood bigger than your frames, and use like 6-8 nails tapped in to the plywood that will hold your screen in place.
The back side of the screen frame sticks out about a 1/4” From the mesh, so make sure your nails are low enough to not hit the mesh. That way you just remove nails and put them in different spots for different size window screens instead of cutting all this wood to hold the frames in place.
Or, if you have really good tape then you can tape your frame down on a table so it doesn’t move.
You really don’t need to make the mesh as tight as you think you just need to get in in there nice and even; if it’s too tight then it will bend the frame in regardless of how good of a jig you made.
Get the mesh over the frame straight and use your roller to roll the mesh in the groves without the spline. Make sure it’s straight and doesn’t meet to be tight. Once you got it straight then start putting the spline in like halfway in around the whole frame.
It should be a little tighter now, but still not enough to pull the frame at all. Now you start working the spline in all the way, making sure it’s once again straight and only tight enough to not let the mesh look wavy.
If you slowly push the spline in, you will be able to tell how much more tension you really need and can adjust as you go.