Just a thought... When you get the pump running on FROG control, try taking the L,N output to the pump from your "smart box" to the L,N in the FROG control (replacing the mains incomer). Forget about the capacitor in the smart box.
I took a photo of my FROG control where the pump wires come in. Looks like L is brown, N blue, and can't see capacitor wire but it would be whatever is left (maybe red). Hook it up like that and your pump will work. Don't worry about the capacitor. FROG will have it hooked up the way they want it.
Did you change the wiring in the control box? All you should need to do is connect the incoming L,N,E to the connectors for that and connect the pump wires to the connector block for that. The brown wire is for the capacitor.
Pretty sure blue is N and black is L in the control box (NOT as labeled above). My recall is that the pump wires are black for L, grey for neutral, brown for capacitor and yellow-green for earth.
These pumps are resilient so I don't think you blew it up. How did you measure 220V across the windings? Make sure you have 220V between L and N on the incomer.
The only stick sold locally is what they label "RB-26". Does the job but inconsistent in burning. Easily flares out and punches a hole and then can be "normal" for a while.
Can't offer a reason against cable trays but don't see any particular benefit for them. If you have junctions, you will still need a box. What maintenance issues would be alleviated by trays versus conduit? Just wondering.
Other than fuses, I don't think I have ever seen a wire melt from over-current (that is not a short). Not saying that doesn't happen, just not in my experience.