Electrical – How to wire a 5-leads single phase asynchronous motor to a 3-leads bidirectional controller

Autistic has kindly identified the legacy motor I would like to recycle as a single phase asynchronous motor (see linked thread). Here is the internal schematic:

(source thread)

I would like to control it with a cheap wireless controller I had bought from Carymart; the issue is that it has only 3 outputs: UP, COMMON, DOWN, as seen on the following diagram.

(source)

I assume the phase shift capacitor is neither in the motor nor in the controller, but a bigger problem is how to wire the 5 leads motor to the 3 leads controller.

I have found this page on the manufacturer's website which is about this exactly, and implemented it in the following schematic, but they haven't said anything about the capacitor. It cannot be an electrolytic type because the current flows in both directions, and since current is always flowing in the capacitor when the motor is running and that it runs for more than 1s (that's a pool cover motor, probably 1min of operation every time), apparently it's not a good idea to have two electrolytics back to back. So I'm stuck.

Therefore I need either a new arrangement, or a type of suitable capacitor. Please advise 🙂

^{simulate this circuit – Schematic created using CircuitLab}