I finally managed to get a better error message:
Initialization [Error] DnaLibrary AutoOpen Invoke Error : DllNotFoundException - Unable to load DLL 'TurboActivate64.dll': The specified module could not be found. (Exception from HRESULT: 0x8007007E)
In my case, the main (host) application is Excel, but the licensed app is my add-in (XLL). It seems that - during RUN TIME - the TurboActivate64 dll is expected to sit in the EXCEL folder, whereas it actually lives in the folder where the ADD-IN resides. This does not appear to be a problem in DEBUG mode. Does any of that make more sense?
I had to make a similar adjustment to access TurboActivate.EXE, which also lives in the add-in folder…
'launch TurboActivate.exe to get the product key from the user
Dim TAProcess As New Process
TAProcess.StartInfo.FileName = Path.Combine(Path.GetDirectoryName(ExcelDna.Integration.ExcelDnaUtil.XllPath), "TurboActivate.exe")
TAProcess.EnableRaisingEvents = True
Perhaps something similar is required for the DLL?