Another attempt to kill several birds with one stone:
The mat drilling contraption is basically the new belt-driven design of the mini-router, with the exception of Z-axis which is also belt-driven (mini-router still uses leadscrew on Z-axis). Dremel flex shaft with the drill chuck and 1/32" bit is mounted to Z axis. The results are rather mixed.

After milling tests, I tried drilling out small hole pattern in the cutting mat (which would make a vacuum table surface for the paper prototyper). Initially I used tiny 0.01" drill bit and drilled a short sequence of holes, only to realize that there would have to be 50x50 grid of 0.01" holes spaced at 0.01", i.e. 2500 holes per square inch. Even without doing the math it was clear that it was going to take forever to drill out 8.5"x11" rectangle on the mini-router, so I switched to 1/32" drill bit, with more realistic 16x16=256 holes per square inch. This would take forever/10 in theory. In reality, one square inch took 10 minutes to drill at 12 IPM which wasn't that bad. Still, at 6 sq.in/hr it was going to take about 20 hours to drill the letter paper size area + 1/2" outside margin.

Here come more mini-router tests - mostly milling soft wood, trying some Delrin. I've run into several issues along the way - they slow down the progress some, but on the other hand they are good learning experiences.
First, the grooves that I initially milled with high speed cutters were about 0.02" wider than the tools. I googled "dremel runout" and found various bits of information, ranging from "Dremel is no good because of runout", to "Runout is much better with chuck as opposed to collet".
After replacing Home Depot leadscrews and finishing the assembly of the mini router, I ran an initial endurance test. The test consisted of drawing 1/4" grid on 8"x10.5" rectangle, rapid repositioning, then drawing 64 concentric circles with 1/16" spacing in the middle of the rectangle. The feedrate was set to 17 IPM (~7mm/s) while rapid movement was set to 20 IPM - not really rapid, but it was the fastest considering that motors stalled at 25 IPM. At 17 IPM the test was going to take some 1 hr 30 min or so. It ran for an hour - the Y axis stalled about halfway through the concentric circles. The rapid repositioning also didn't work too well since the circles were shifted relative to the grid in both X and Y - I have not yet figured out by how much exactly.
The video is 16x realtime. Y axis stall happens in the very end at 4:20.
This is mini-router assembly in progress. The Y, Z and X stage are already assembled, working on the base now. I wanted to do a video timelapse of the whole thing, but as I went into several dead ends where I had to go back a couple of steps and re-assemble or re-align something differently, I thought I'll do clean timelapse when there are documented steps.
I've also had several issues with the assembly that aren't showstoppers but are still important:
Milling plywood was relatively easy. Plastic - a bit more difficult. First, I tried cutting shapes out of black 1/8" thick sheet of what turned out to be polyethylene, according to this plastic id table. I used the same high speed cutter as for plywood - Dremel #194, speed setting 4 and 0.03" depth passes at about 9 IPM. There was a lot of plastic swarf. Then I tried milling a 3/8" thick cutting board made from HDPE. The stuff started melting and forming blobs around the bit, even though I used recommended speed setting (4). After experiments with speed and feedrate, and online research (good plastic milling info), I switched bits. I wanted to cut gears for RepRap extruder out of HDPE, so I got some small diameter bits on eBay to try.
Finally, here goes: minirouter and first tests with Dremel on plywood. The router had actually been assembled for weeks - it only took me several evenings to assemble it, but few problems came up and I spent time trying to fix them, then fixes/workarounds resulted in new problems and so on. The same flaws and weak spots mentioned in the previous post still remain in the design. Couplings is one of them, and non-alignable leadnut is the other.