I thought I'd heard of a 3DR variant that used the extrusions for linear motion.

Does that ring a bell for anyone? Can you point me to it?

I believe it is either the Kossel or the Cerberus that use the extrusions for their linear motion. You can probably just use their vertical carriages instead of the ones with the 3DR to use the extrusions.

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There's also the cherry-pi and a number of cherry-pi custom build/derivatives like the one AndyCart made.

There's no reason why you couldn't do this with a 3DR, you'd just need a 20x20 carriage like Andy's (Cherry Pi).