Luke11CNC Build Log ,I'm so naïve

[Jonathan]

So then for that very reason NO it doesn't make them better.!! . . . .They will only be better for shortened period of time, obviously how long depends on Belville force, but they will wear sooner with the ultimate result of a wornout knackerd screw.

I think the spring method will be better for longer as wear with the double nut will lead to more backlash, whereas wear with the sprung nuts will not have much effect. It will reduce the preload a bit, but you can adjust it so it guarantees that backlash is eliminated. Which is pretty pointless on a router anyway...but I know which method I'll be using when I convert my lathe/mill.
Either way for hobby machines they are used so little (relative to in industry) than wear on the ballscrews/nuts is negligible. If you've used it for long enough to wear out the ballscrews then you've probably made enough money to replace them.

James: That not being quite square is one reason that I suggested you used triangular plates from the X-bearing mount to gantry side. They will stop the deflection.

I cut the slots in the gantry sides on my router as they wouldn't fit on the mill. The bad had been surfaced recently, so they shouldn't be far off ... if you want me to skim the bearing mount plates to get them square that's not problem. I meant to do it anyway but forgot.
Bear in mind SBR/TBR type bearings will tolerate some rotational misalignment, so will it make a difference when the machine is running? I don't think so, but I'd still add reinforcement triangles to make sure.