Rotary compression tests require a dedicated tester.
If your mechanic doesn't have one, find one who does, are there any mazda dealers close to where you live?
As a last resource you could use a standard compression tester with the purge valve open:
crank the car for a set amount of seconds (5-10, whatever) while counting the revs somehow (obd gauge, hear, whatever). You must know at what rpms the test was performed
read the spikes on the tester's gauge.
Pick 3 consecutive spikes and compare them to the specs present on the workshop manual. Adjust to the reported rpms and.. job done.
Of course this is a highly imprecise method but as a last resource could still be worth something.
You could also use other empirical methods, like heavy premix etc but they're still a shot in the dark at times.
Is your fuel filter dirty? Is your maf clean? is your catalytic converter clogged? These factors could very well be con-causes to your hot starting problem.