As a data point, redemption in J with a BRUV as a GGL, op-up to F overnight ahead of a 7pm departure (I had selected a seat but hadn’t checked in).

In answer to your question I think there are too many variables to predict, and upgrades happen at many phases (check in opens, staff/duty travel loading overnight, airport check in, flight close) - but leaving check in till later if you have a seat reserved doesn’t sound like a bad idea.

Your best shot at a paid-upgrade is during the check-in process, which I believe you can back out of if you don’t get an offer that you like. So no harm starting check-in a few times to see what the price is like.