Yes, 5mm poles are too flexible for going through a ceiling void horizontal. Max 2-3m before the tip drops down and gets snagged on the ceiling bars / insulation. I'd get 8mm if doing it again.
And drawstring didn't work. Cable kept getting snagged. Better way was to attach the cable directly to the rod with tape.
Installing the charger itself was easy. Project EV Apex 7. It's literally one cable, three connections each end. My consumer unit already had a 32amp RCBO installed with common neutral for the charger, so was just a matter of pulling the cable in and wiring it up.
The Apex 7 doesn't need it's own earth, has lots of built in fault detection functions, so I'm confident it's all as should be and safe.
Main motivation of doing DIY was not money, but time. We bought the car last Monday, only way to charger is at public fast chargers at ~65p/kWh. Couldn't get an electrician round any time soon.