Call reservations and ask for the certificate to be pulled/applied and have the ticket reissued.

I received a new confirmation email that had a new ticket number in it. For a bit more detail, I made the booking around 11:30pm, when I woke up at 6:30am I had been upgraded but didn't have the confirmation, and then at 11am received the new confirmation email. So I think the upgrade itself happened within a couple of hours but it took about 12 hours to fully be re-issued.

This worked out well for me. I had just used my expiring SWUs for a domestic trip this weekend, so was unable to use those. However, we had booked a leisure trip to Venice in August with a fully refundable fare. I cancelled those and re-booked using the PE fare for a decent savings. My wife is spending more time in Europe on the way back so on a different PNR (she has God Status), the SWU for her also cleared within a few hours last night. All in all it worked out well for me.

God status or Gold Status? I'd love to have God Status too, on AA.

Also, not sure if anyone can answer this. If you get confirmed J seats from this promo, but then need to move the flight dates to September, hypothetically, what are the limitations of attempting to do so?

From the limited research, I think the C space has to be available in September, but not 100% sure. Just curious on what the limitations / conditions are, if the flights need to be changed to different dates, once you have confirmed J seats.

Very helpful, thank you. As an aside, what is your hotel strategy when traveling for these trips, given you're already Marriott Ambassador?

I'm Marriott Titanium, but mixed on staying at over-priced Marriott properties in Asia & Europe, just for the free lounge access / breakfast for 2 (my family travel party will be bigger than that), and maybe an upgrade to a suite (although not guaranteed), vs using AA hotels to get a suite at a non-Marriott property and buy our own breakfast as we choose. Deciding between giving Marriott more money for more devalued Marriott points, get some limited perks in Europe / Asia, or use AA hotels to get more LP to keep my LP points higher for maximizing odds of free AA upgrades domestically or SWU upgrades internationally.

No different than any other time you want to voluntarily change flights with a confirmed SWU upgrade. Yes C space needs to be available on the new flights if you want to stay in business class. Otherwise you change to Y or PE and get on the waitlist.

Joke's on AA... An August trip made sense, so I browsed for PE flights and quickly found some with regular SWU availability -- then booked Y for about half the price of PE.

Really interesting. I just checked ExpertFlyer for the routes I booked PE for, and found zero C seats availability + or - 3 days of the dates I looked at.
Did your SWUs already clear? What routes?

Congrats on finding the unicorn that is confirmable in advance upgrade availability!

Yes. EZE.

I like they will let you fully cancel the PE ticket regardless of fare class for about a week if this PE to SWU promo fails.

I am sure all of the downside of this promo (min PE in the future, etc.) are all possible, but all anyone can do is take advantage for those who have SWUs.

I think we all agree AA is still a massive leader in normal award redemptions so there is downside to all of this (less inventory, etc.), but as long as there is a business class seat for sale, I can't fault the simplicity of the offer. That seems a bit rare among airlines. Obviously, that is why the window for the promo is small both to book and travel because just in case AA made a massive mistake in the promotion cost, it limits the potential problem (which I think is why it is limited to less than two days to book for the system to scan PNRs and upgrade).

+1
If nothing else, it saves a potential PR problem -- the last thing AA would want is to have the negative press of a bunch of people jumping on this to buy $1400 one-way tickets only to get rejected because the seats ran out. Odds are it won't be a problem for a two-day window to book tickets for August, but you never know, there could be 100 EXPs all trying to grab tickets to Lowlands on the same handful of flights...