It's more iron than I could deal with. Besides, using hole
saws that I have (up to 3" ) it looks like using one of these
high power, high torque tools would prevent a reasonable
amount of 'nibble control' afforded by straight vertical tool
setup.

If the actuall cutout size is listed at 3 11/16, then
which of the hole saws would be the correct one to get?

I have noted that if the hole saw is listed at 3", then
3" will be the final cutout. Measuring the hole saw itself
shows that the units are made to account for kerf removal.