We have a lot of wild horses in Australia - they need regular culling.
My first thought was 3 or 4
♠ - I should have stuck with it.
My thinking was (surprisingly) similar to Mike's.
I wondered if 2NT was Leb (not alerted) and 3NT was a failure to accept the transfer because West thought 2NT was an invite with a spade stopper.
Given that partner had passed twice (and he isn't very conservative) I figured EW had around 30 HCP and defeating 3NT was the best outcome.
I was also worried that opps would run elsewhere if I doubled.
3NT-3 was 54%; one pair took 3NT-3X for 79%
Here's the full hand: