Welcome to the forum, I would love to see a photo of this birthday cake when it is finished, it sounds amazing!
There are three main ways we can slow a brushed motor like that down:
Add a gearbox as you’ve suggested, this is probably the simplest to implement, the downside is you’ll need to couple from the gearboxes output shaft to your ski lift, which is a slightly different size from the motor output shaft. Probably a minor obstacle given you’ve already got everything else working.
Run the existing motor at a lower voltage to slow it down, I don’t recommend this as it makes your motor more likely to stall and since your motor is already running at 3V it’s quite low already.
Use a motor driver to add variable speed control to the motor. Motor drivers are relatively cheap for this size motor (around $20), but they will need a microcontroller (also <$10) to send signals to them to tell them when to speed up or slow down. You can get motor controllers which are very similar to motor drivers but also include the bits that allow you to control it using a knob, or USB depending on the motor controller. Motorcontrollers start at around $130 so we can rule them out as an option.
Unless you’re keen to add a motor driver and microcontroller purely for the experience of learning how, the only real advantage is being able to wind the motor speed up and down at will.
I think the gearbox kit you’ve linked is your best bet.
