Sorry, but I am doubting this DLLs (even though they're embedded in the exe) part. How did you determine that this embedding occurred correctly?

On ActiveState, I manually installed this SSL stuff and wound up putting the .DLL's into a bunch of places so that PerlApp could find them. C:\Perl\bin, Windows, \Windows\system. I remember this being a mess. I have libeay32.dll in C:\Perl\bin and both of these DLL's in the normal Windows places for the other DLL's.

Sounds like you don't have these DLL's in the .exe otherwise they would be found and used even to the exclusion of any .DLL's in the .exe directory.

by definition any "standalone .exe" will run without any .DLL's on the target machine at all!