Pleased you got it sorted mbell.

Mick, I'll add your tip to the repertoire

I take it your referring to the Woodruff-type key (the lozenge shaped key that fits in a slot on the shaft)?

I'd try the escalating levels of force routine.
1. Soak it in Plus Gas penetrating oil (if you can find it), or GT85 / WD40. I often use s mix of carb cleaner & GT85 – the carb cleaner is highly penetrant and helps carry the lubricant into the tiniest of gaps.
2. Repeatedly tap it gently a couple of times each side to help work it loose.
3. If that doesn't work I'd get a blowtorch on it and heat up the shaft. The heat causes the shaft to expand and helps break the seal.

It's certainly something else to go wrong. I've seen quite a few on Briggs engines and the thermostat side of things seems to work OK by and large. But it's the associated linkages that ham-fisted types sometimes bend and I'm definitely not a fan of that finicky black plastic flip-over-centre choke flap actuator lever thingummybob

From what I hear, the going rate seems to be about £40 – though it may vary dependent upon circumstances and location.

I do ultrasonic cleaning as a matter of course as part of a service. I'll strip the carb, including the jets, and put it in the tank whilst I get on with other tasks. When the carb has finished "cooking" I'll rinse it, blow out with the airline and reassemble.

(And yes, Mick, I love Honda carbs too