I think the optimal strategy is:

1) Check in online ASAP (24 hours before the earliest departing segment)
2) Print out an online boarding pass (or save a copy of your mobile boarding pass)
3a) Subscribe to EasyUpdate and you'll probably be told when your upgrade clears; also,
3b) Periodically try to check in. If you get a message that says The itinerary your PNR has generated an error., you're golden!
4) If your upgrade cleared (3a or 3b), go to the airport early -- you're going to need some extra time with an agent. If your upgrade didn't clear, skip ahead to step 6.
5a) Get to the front of the ticketing/checkin line (this is slow). Then convince a ticketing/checkin agent to offload you from the flight and put you back on the flight. (Depending on how sure of yourself you sound, this can be very easy or painfully difficult. The staff at SEA understand what I mean when I say "I need an agent's help checking in, my upgrade cleared after checkin and I need to be offloaded and re-loaded", but putting that many action items in a sentence may confuse the heck out of an overwhelmed agent at some airports.); if this fails or the line is too long,
5b) Go through security with the online boarding pass you carefully saved at step 2). Then convince any gate agent (not necessarily the one for your flight) to offload you and re-check you in; your upgrade is now cleared. Note that you *may* still need an agent's help to select a seat or change seat assignments -- in my experience sometimes the EasyCheckIn machines now work, and sometimes they don't.
6) Upgrade didn't clear? Wait it out at the gate with your un-upgraded boarding pass like everyone else

Note that the optimal strategy is slow (there's a step where you might want to talk to an agent before the flight's counter is open) and risky if you don't have a printer handy: it's possible to be checked in, unable to cancel your checkin, and unable to get a boarding pass without waiting in line and talking to an agent before security.