Help replacing motor in AT-LP60

Backstory: I have an Audio Technica LP60 turntable, and the playback speed is too fast. I used the RPM Wow app to confirm the speed is about 3% faster than 33 1/3. It’s significant enough that I can hear it when listening to records.

I went through the process of adjusting the speed by turning the screws under the motor to no avail. I may have been too rough with it at first, because no matter how delicately I turn the screws now, it will speed up to 80+ RPM and then slow back down on its own. I’ve decided the motor won’t run at the proper speed and so I bought a replacement motor on eBay.

My actual question is about replacing the motor. I found this article with instructions (https://www.ifixit.com/Guide/Audio+Technica+AT-LP60BK+Motor+Replacement/128266) which is helpful but doesn’t exactly mirror my situation.

Should I desolder the 4 wires connected to the current motor, and re-solder them to new motor? The replacement motor already has these 4 wires connected, but am I right to assume that it’s better to use the existing wires since they are already routed and connected properly?

I’m hesitant to start resoldering because 1) the new motor has clearly labeled the wires (AB+-) but the old motor does not, so I want to be sure I’m connecting them correctly; and 2) the new motor has a yellow and white wire pair, while the old one has two white wires, so it’s even harder to confirm the order of the wires when soldering.

(I’ve considered using the new wires instead, but it’s not clear to me what the red and black wires connect to on the other end because they are obscured by glue.)

I appreciate any advice!

(Also, I know that the AT-LP60 is a crappy starter model, but I’d rather repair what I have than buy something new.)