Did a little more testing and this is what I found. If I use the "Insert from file" feature to combine a cover sheet plus 3 AcroForms (inserting each file one by one), eveyrthing appears to work. However, if I use the "Combine via Acrobat" feature I run into the issue of fields disappearing once combined.
I shoudl also add that perhaps the issue had something to do with the fact that I initally produced the cover page pdf via Photoshop "save as PDF". Perhaps that contirbutted to the structure issue despite it being a PDF...maybe under the hood things are structured differently. Who knows.
Just FYI for others: What appears to be working is using the "Insert from file" option vs "Combing via Acrobat". Also, if you are including a non-AcroForm PDF, be sure it a traditional vs. saving as a PDF from Photoshop.
Alot of this may be a fluke, but it seems to fix my issue - for now.