Congrats! Glad you got it going!
Having AICarriers under the P3D folder may be a quirk of P3D3.1, since I have my AICarriers no where near my FSX-SE folder, and it works fine in the EXE.XML file. From what I can tell, your pathing was correct, at least from what you showed as to where it was located, but again, maybe a quirk peculiar to P3DV3.
A way to test it is to put vLSO (presuming you have it) outside of the P3D folder someplace, like maybe your Utils folder or on your C:\ drive or whatever, and see if the EXE.XML will load it up. If it won't, but does if you move it the P3D folder, you will have a certainty about it. You will know for sure it just a P3dv3 quirk.
Make certain you have admin rights to the folder it's in too, like your Utils or wherever. That may have, in some odd way, have been you problem.
I'm just grasping at straws, though.
Glad you got it going, anyway
Pat☺