I'm used to approaching these problems from a slightly different angle. There are two simple cases that can be used to establish guide points.

If you have a load that is purely inertial, the optimum gear ratio (to minimize I-squared-R motor loss) is found by picking a gear ratio which matches the reflected inertia of load and motor. At this point, on every acceleration you put just as much energy into the rotor inertia as into the load inertia.

In contrast, for a steady-state load which is all friction (e.g. a mixer such as for paint or food), a gear ratio which balances friction loss in the motor with the load friction will minimize the armature loss.

Most applications have live between these points, and these optimizations ignore gearing losses and expense and noise, but they can serve as guide posts.

There's also the issue of separating winding choice from gearing choice. For each candidate motor there exists an optimum gear ratio which will minimize the heat produced when driving a given load (friction and inertia) over a given velocity profile. That gearing can be found by trial and error in a simulation. These aren't crazy difficult simulations (can be done in a spreadsheet) but do need to take temperature dissipation and change of motor performance with temperature into account. Once that gearing is found, the V-I requirements of the motor at that gearing will be known and then winding adjusted to fit requirements of driver circuitry (i.e. trade current for voltage).