I have seen many clever ways to attach the drive screw to the axis'. The more durable the connection, the better. I took a 'cheap-and-dirty' approach that I will no doubt pay for later.
I used a coupling nut and attached this to each of the three axis assemblies.
I cut matching dados into one part of the axis assembly and a smaller "cover", shown at the left. I sized everything for a very snug fit. Using a chisel or sharp knife, I notched the bottom of the dado (image on the right) to accept the point of the coupling nut. I added liberal epoxy around the coupling nut and glued and pressed the two parts together.
I selected a dado over drilling through the piece because, as I was using plywood and not MDF, I couldn't get the drill bit to track perfectly straight through the center of the plywood.
Note: for the X-Axis, I just did the dado and epoxy with no 'cover' glued and pressed over the coupling nut. the epoxy just broke loose two nights ago. I will design a much more robust attachment.
To the right is a photo of my Y-axis drive screw. You can see the dado in both pieces.
Backlash: Yes, I am aware that this type of nut is not ideal and that it can fall prey to excessive backlash. As the first version of my router is my "proof of concept", and I'm not machining to the micron, I don't currently care about the tiny bit of backlash present. I must say, however, that it's not too bad. We'll see after 10,000 cycles how it looks and feels!