Can I apply for a multi-entry Non-O retirement visa from the UK without waiting a year?

I think you are confused. A multiple entry visa is a 6-month or longer visa, that gives you a full entry stamp every time you enter. There is no such thing as a multiple entry non-O visa, as a non-O visa is only a 90 day visa.

I believe you are asking about a re-entry permit, which is nothing like a multiple entry a visa. A re-entry permit just prevents your visa entry or extension from being cancelled when you leave Thailand. The time on your stay still ticks down while you're outside of Thailand, and you have to return before the stamp in your passport runs out to apply for your next extension. None of that applies with a multiple-entry visa, because you get a brand new stamp with a multiple-entry visa.

For a 90-day non-O visa, and then the 1-year extension, you can apply for a re-entry permit within Thailand. You can apply either at your immigration office or at the airport as you are departing Thailand. There is no requirement to wait any amount of time to apply for a re-entry permit, and there is no minimum amount of time to be in Thailand.

You could enter Thailand on your non-O visa and get the 90 day stamp, then leave with a re-entry permit and return 89 days later to apply for the 1-year extension, purchase a new re-entry permit for that extension, then leave for 11 months and return to apply for your next extension.