My goal is to have 20A receptacles in a particular spot in my garage dedicated to power tools (such as saws) whose motors can be configured for either 240V or 120V, with a switch as a handy second level of safety (like when changing saw blades but it's inconvenient to unplug the machine). I'd prefer for the 240V and 120V receptacles to share a box.
Would it be correct/safe to install a 20 amp two pole GFCI with load neutral, then use 12/3 to power NEMA 6-20 and NEMA 5-20 receptacles sharing a box?
I would add a quality 20 amp double pole switch (or 30 amp... apparently some are derated for motor loads) in a convenient place in the garage.
Then I think it would go like this in the box housing the receptacles: black and red to the NEMA 6 receptacles; on the NEMA 5 receptacles I'd break the hot tabs, wire black to half of them, red to the other half, and pigtail the neutrals.
I understand the NEMA 5 receptacles will make a MWBC since they share a neutral. I'm not sure how the definition of MWBC overlaps with the NEMA 6 receptacles being in the mix. It also seems strange to mix 240V and 120V in the same box, but I'm totally new to all this (including 240V tools) and have seen other answers say that's okay.
If this is an okay method then I'll run the numbers to see if this method has good bang/buck for me versus other setups.