Is providing a slow response to journal reviews a common/good strategy for minimizing the number of review requests?
I can imagine someone purposefully delaying reviews, but in my experience it's not a widespread or standard part of mathematical practice, and I haven't heard it offered as common advice.  I don't think referees have an obligation to inconvenience themselves to finish a review as quickly as they can, but it seems bizarre to deliberately delay when it would have been convenient to complete the review earlier (or, worse yet, when it was already done but not yet sent).

I don't see a real risk here, or a need to avoid review requests.  There's nothing wrong with turning them down, and you can use a vague excuse like that you are already busy with other refereeing and don't want to cause unnecessary delays for this submission.  In fact, a prompt reply will be appreciated; it already puts you ahead of the people who require reminders to reply to referee requests.  (When a referee declines quickly, there's almost no cost, while it's annoying if I send several e-mails over a period of weeks but never hear back.)  From my perspective as an editor, I'm not looking for people who will complete a review as quickly as possible.  Instead, my ideal referee is someone who is responsive and reliable, who promptly lets me know what they can reasonably do and then does it within the timeframe they estimated.  If they do that, they can turn down as many requests as they like.