Clients come to us a month in advance, but wait to book because they want to wait to pay. How can we get this to not effect our scores?

Just archive them, use a reason like "didn't respond" so it doesn't hurt your ranking. Your clients will be able to complete the booking closer to the actual sitting date, provided you are still free, even though the request has been archived by you.

Archiving will free up your calendar but this question is about the Performance Scores. Archiving will not undo the "damage" to your Performance Score. The good news is the Scores are in constant flux so unless there is many months lapse between the M&G and the Owner paying for the stay any "damage" would be fairly short lived

Where the problem comes in is that Rover suggests Owners contact 3 Sitters... which obviously sets up 2 Sitters to take a hit to their scores. I've actually had people tell me at M&Gs that they'd contacted 2 other Sitters but were hoping to only have to do one M&G. Which of course is great for the person who gets the first M&G, not so good if you're one of the 2 people who Rover put in the position of having to bear the brunt of an unbooked stay.

I have customers call or email to my private email what dates they want in advance and I put them on my "private reserve calendar". I notate the calendar a couple days prior to their date(s) & contact the client for confirmation and send the booking request on the date they want it sent. That way they are reserved and I adjust the rover calendar +/- on those dates. If their plans change, no problem and I adjust my rover calendar again.
But, as Karen & Walt said, if they don't pay within a short time I archive. When they are ready you will see a notice from your customer above the archive folder and you can make it active again or just "accept" from the archive.