Sage resolved, hopefully: I spoke to someone last week on the phone who was raising this as a complaint on my behalf. Didn't hear anything back so did live chat this time on the website, apparently my smart meter readings were being received just fine the whole time, I was just switched over to billing via estimated readings for no apparent reason. Utterly baffling. They've switched it back onto actual usage now.
You were correct the first time, the company is genuinely inept. Honest to god, one of the worst companies I have had to deal with.