Making a dumb cooker hood smart

iFan 3 is here… I already took a copy of the original firmware just in case.

This is the wiring diagram for my extractor hood:

Brown wire is live, blue wire is neutral, on the “push button”, first L with yellow wire goes to the LED driver for the two lights under the hood. Second L is live wire from mains. 2 is speed Low, 3 speed Medium, 4 speed High.

iFan has these wires: L (live input from mains) N (neutral input from mains) and three output wires: COM (neutral output), FAN (live output to fan, which varies values to change speed), LIGHT (live output for lights).

I know how to wire the lights. My idea is to use the black wire (fan speed HIGH winding) on the FAN output of the iFAN 3 and then it will vary the speed through voltage difference? My understanding is that’s how it works? I know the capacitors on the iFan will have something to do with it…

The motor has 7 wires, two (yellow and brown from the motor) come from a large cylindrical capacitor that I assume should remain in place, in addition to the capacitors from the iFan? Then wires white, black, red go to different windings to control speed. The live from the mains seems to be bridged to each speed within the push button control. From my observation it seems like the medium speed is achieved by bridging two windings (medium and low). Highest speed is its own winding, which is why I was planning to use this on the FAN output of iFan and the neutral goes to COM and with the neutral for the LED driver for the hood lights.

The motors are either one or the other:

Can anyone with experience in motors comment on whether there is any problem with this plan?

Edit:
I did like I said above and it works, but only on the top speed. Any other speed and the extractor can be heard to struggle and I’m sure that’s not healthy for the motor at all. I would like to retain all speeds if possible and was wondering if anybody had any ideas!? I thought about using a relay board but how to trigger using just one wire from the output of the iFan?!