Thanks for the suggestion, draconus. I took a look at the log file and searched for anything relating to the F-15 and found an error line referencing the F-15E-CPT.dll file being blocked by bitlocker encryption. The drive that DCS is installed on is not encrypted, but another division on the same NVME was (nothing DCS related in there). I disabled the encryption of that other drive, and then booted the game and was able to load in fine - so it appears that it's fixed.
TLDR solution: Having bitlocker encryption enabled on the same physical drive as your DCS install will block loading of the required .dll file.
Appreciate your help!
iamface's post in Not able to access module despite showing in-game (Open Beta - SP, MP) was marked as the answer