As an update, I double-checked with Amex and they said the advice I'd been given by their chat representative was totally incorrect and I shouldn't change my account address during my trip.

The person I spoke to said she'd always managed to get by by using her hotel zip code. Starling Bank said I should use 99999. I've read elsewhere (as suggested below) that padding out my home post code with zeroes was the best option. So.... I'll see what works and what doesn't, and will report back. I've postponed buying the flyaway bus tickets for now, as I may not need them. In fact I may not need a zip code until I hire a car and try to fill up with gas.

In the past I've had varied luck, it really depends on the merchant.