@Dave you've got all the same questions that have been running through my mind as I pondered this conversion.
I started my thought with 4 screws, 2 rods as I described in the first post and @csorrows also described thinking a precision component so I know the x-y is straight .....but then thought the stock rods would probably be too small dia to do much of anything but flex against the 4 screws. That got me to either find larger rods or just leave them out and see how it goes.
.....which got me back to the stock design should work if the bed mount plate is rigid. The y has 2 motors and never gives me trouble because the assembly is rigid enough that the motors couldn't possibly flex it enough to be out of sync even a single step much less a few mm.
I'm now thinking I should just stop thinking about band-aids and make the thing rigid. Today's though is to get some 1.5" aluminum angle at the hardware store and turn it into a bed mount., I think what they have is 1/8" think which should be enough....for sure 1/4" would be rigid enough but no sense in adding weight that isn't needed so I'm thinking I'll try the thin stuff and see what I get.