Since you have specific routes in mind, my suggestion is to subscribe to ExpertFlyer (you can even use a free trial if you want) and do an "Upgrade and Award Search" for C inventory on AA for each specific flight you are interested in. Set the "Connection Preferences" control to "Direct/Non-Stop Only" and click the "Exclude Codeshares" box. For the date, start with a date four days later than the current date, and set the control to "+/- 3 days" which searches one week (the date you enter, the three days before it, and the three days after it). You can also set the return date the same way (or leave it blank to search one way at a time). After seeing the search results, click "Refine Search" and change the date to be exactly one week later (easy to do by clicking the calendar icon). Repeat this for the full bookable window of 331 days. Then, repeat the entire process with a different flight. It can take a bit of time, but it's the best way to see what C availability is like for flights you are interested in. Of course, AA can remove or add C inventory at any time, so doing this is just a snapshot of the current availability, but it should give you an idea if space is likely to be there when you need it.

You indicated that your alternative would be to credit your flying to AS and use its miles to book award flights in business class. You can use Expert Flyer to search for award inventory in business class on some AS partners (you can, e.g., search for award inventory on AA but not on JL).