[corobo]

In your opinion would be be alright to meet in the middle? A sort of no-frills cancel process with a survey/question after the cancel's gone through?

That way your cancel's done and dusted but with the option to feedback if you fancy it

[reificator]

It still comes across as clingy, but it'd be a huge improvement over putting it before.

I've seen a few sites that don't make it clear that you have successfully cancelled and act as though the survey is still required, so don't do that. Make it clear the user has finished cancelling and this is an extra step they can take if they'd like.