I've been through this same process recently. 8 days for a response from hello@ email address, saying to use the online web form. So the only way is to call, or try Twitter DM. Oddly on the call they didn't seem fussed at all about customer circumstance, more just wanted recordings of explicit customer confirmation to take the action. Like they've decided to take on lots of fixed-rates deals even if that's bad for the customers panicking ahead of the price rate cap hike.
If moving electricity-only the intermediate tariff is quite pricey (42.7 p/kWh for me, 10 month fixed) but hopefully won't take long to enable Octopus Go and was advised to call them on the day of new provider start. There's also an account dashboard web link to achieve this. Around 17 days to switch.
Referral can be applied after sign-up in their online account, and wasn't asked about this on call (or even if I had an EV, but the 10,000 kWh/year consumption they did ask for might have been sufficient hint). I was hoping for a secret link, but none was forthcoming. Email support advised that it has to be done by phone to confirm their “terms and conditions”, even though I gave all the information they needed in the original email.