I've never heard of a manual trans with an oil pump to force lube the gears and bearings etc.
I know that on an automatic it's the front pump that needs to be turning to pump ATF through it.
Maybe it's that I've been out of the loop on manual transmissions of late, but as a service manager at a Chevy/Pontiac dealership for 15 years, we always allowed a manual to be towed.
So what am I missing here?
I see a lot of RV people tow their Miatas on flat fours, no tow dolly.
The only thing I can think of on towing on a dolly with front wheel up is that the trans fluid may not be in the right spot to get circulated by the gear splashing.
The more likely reason Mazda says no on the towing is a legal one. Ford and Mazda have the same transmission in one of their joint venture cars and Mazda says not towing and Ford says yes to towing; the same darn transmission.
There are two ways I would tow a M3W, again my opinion only, I would make up a tow bar and tow with all three wheels on the road with the steering wheel loose to self steer. The other would be a dolly, but modified for a center wheel. I would then back up onto the dolly and strap down the rear wheel and tow with the front wheels on the road. You would have to strap the steering wheel solid so the wheel will not turn, but that's not a big deal.
I saw on the RV forum where guys towed their Miatas thousands of miles and many different year cars without any issues.
Now with the M3W's, warranty enters into the equation. If Morgan says no and you do tow and something happens later to the trans, they could refuse coverage.
Over the years I've towed many vehicles from dune buggies to my 4x4 1/2 ton trucks behind my motorhome and never had any issues.
So good luck with the towing and it's up to you to decide how you do it.
