Chris,
I've owned 4 Cubs with the M-18 and they all shared that issue, to some extent.
I had the starter rebuilt on a 1862 and never had that symptom reoccur.
I currently have an 1872 that will sometime just not kick the gear into the flywheel without repeated attempts. I started leaving a battery tender on it to assure the battery is always topped off, that seems to help.
I believe you can loosen the motor mounts on a 1872 and remove the started without needed to pull the engine.
Good Luck,
Curt