I think you've already answered your question Chris.
It sounds like a simple box at the rear of the base will do the business. You will need to bring the shaft out to one side to drive the filer and make a hole for the speed control. Bring the power lead out the back and make sure it's well anchored. You could make the box out of sheet metal but I find 6mm ply is very convenient for this kind of thing. If you think ventilation is an issue, make some slots in the back. Make the box large enough to take the parts and to look like it was designed (rather than just knocked together) and I'm sure it will be fine.
I've just converted my 1/4" Cowells drill to DC drive. I needed to mount the motor and after faffing around with various bits of angle iron, finally just made an open box to hold the motor and give some adjustment for belt tension. The PSU (which sits behind the drill pillar) came in a somewhat flimsy plastic case, so a ply cover will be used to keep out wandering swarf. The motor didn't have 'feet' as such, so I printed a 3D saddle to hold it (designed in Open SCAD).
It's all painted etc now and looks fairly neat and seems to work – I've still some things to tidy up. Here is the open ply 'box' before painting etc. A 2x4ft sheet of 6mm ply is not expensive and can be used for all sorts of jobs like this. The slots were drilled at each end and then just cut with a jig saw.
Try it and if you have problems, then change or improve it – it will probably be fine but maybe not. Either way you will learn what is required in practice, without breaking the bank or spending loads of time on an overkill. 
Regards,
IanT

Edited By IanT on 09/11/2020 17:03:23