Building is a great option.
I use this one, but I got lucky because it perfectly fits a Define Mini C. https://www.amazon.ca/gp/product/B07QPJZVQ1/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&th=1 There may be similar ones available wherever you are.
No worries. This is the one I use. Amazon Canada though. Perfectly fits a Define Mini C. You'd have to check against the dimensions of the R6. https://www.amazon.ca/gp/product/B07QPJZVQ1/ref=ppx\_yo\_dt\_b\_search\_asin\_title?ie=UTF8&th=1
This one seems neat, I might go for something similar
https://www.amazon.com/Bestier-Computer-Holder-Caster-Wheels/dp/B07QPJZVQ1
Lifted a bit off the ground - yes for sure. I personally use one of these: https://www.amazon.ca/gp/product/B07QPJZVQ1/ Check your case dimensions carefully though. I use a Fractal Design Define Mini C, and this cart is perfect for that.
Mounting under the table is of course doable as well... just depends on how handy you are. In that case you'd definitely want to go mini-ITX.