Biggest thing to keep in mind is that using award miles or SWU's is an either/or situation. You can either use award miles for a 'free' ticket, or you can buy a ticket and use a SWU to upgrade. You can not do both on the same ticket. And while award miles can be redeemed on partner airlines, SWU's can only be used on American metal.

My wife and I 'argue' over this annually. I want to use up SWU's (and also earn miles in the process), and she just wants me to redeem miles for 'free' tickets. AA could help my marriage if they'd just let me use both on the same ticket

As others have pointed out, award seats (at least at the saver level) and upgrade seats are generally hard to come by without a bit of searching and patience.

One other option is to look at AA Vacations, which combine air + hotel. They often have really good business class fares (below what you'd publicly find), and you can just pick the cheapest hotel room and not use it. Those tickets are SWU eligible. Then you could look at (with your fingers crossed) finding saver awards for the other 2 tickets, or buy the other 2 tickets through the Chase portal.