From the way TRIPCASE works for me (they ask my permission to link with my account on GOOGLE (and GMAIL)), aren't they just constructing the receipt from my email [e-ticket] confirmation but NOT from AA's database?
Hence if all my e-tickets are still intact on my gmail account (GOOGLE gives me plenty of space, so I don't delete anything posted in the last 5 years [at least
]--why would I need TRIPCASE?
TripCase is owned by Sabre and has direct access to Sabre reservations. In addition to importing reservations from email (and, as you say, just extracting the information from there), there is functionality for direct linking to a sabre booking. Use the "link a booking" button (with chain-link logo) and enter the PNR. From there, go to documents and it will have all the eTickets that have been issued in that PNR. Also, if the PNR is active, it will have arranger view where you can see things like waitlisted segments (which is great for verifying upgrades are actually waitlisted when you hang up from requesting one).
why would I need TRIPCASE?
Try what I noted above (e.g., for your PNR with SWUs waitlisted) and look in the documents section. Trust me, you won't be asking that question anymore!
The image below is an example of one of my trips in TripCase which ended up having 19 eTickets (four tickets with many reissues). In TripCase, the ticket numbers from all 19 can be seen together. You can click on each one to get a receipt. This, in and of itself, is a big improvement over the print receipt option in AA.com (when it works) because all the etickets/receipts are there for the whole history of the PNR, not just the current eTicket. In addition, unlike the print receipt option on AA these are receipts for the full value of the ticket, not the incremental value of the reissue. In other words, you do not need to piece together several receipts to show what was paid.