You have right idea for the belt, is not a great idea, gears are better.
If you connect the shaft of two motors. It is obvious they are connected in series. Like this the same current pass through the two motor and theirs torque are equal. If you connect in parallel, the difference between internal resistances generates waste. One motor wants to run faster than the other and the other brakes the first.
I spend a little time to draw the twoo schematics for serie or parallel wiring of twoo DC motors.
I hope have time one day to explain the benefit of serie connection for connected safts.
Serie - parallel wirring of DCs motors.
Her you are:
The math show that in serie n the speed of shaft is capable to be the same for the twoo shafts without wast.
In parallel mode n1 is not equal to n2 then it work not at the optimum.
Maths to present the adventage of serie wiring for connected shafts.