Thank you for the save game.
First, if you have unpatched smac version, they most likely this is a bug, that will disappear after patching the game.
Other option is that such units might be pre-defined, but they do not show on F1 screen, so it's probably one of early bugs, or even features, that developers abandoned trying to balance gameplay.
I have patched smac to version 5.0 and this is what I saw in unit workshop:

Note, this is when I have mouse over the low small tile slot for the AAA transport, it shows AAA in lower small view, but the larger upper one shows no AAA.
Then when mouse is
not over the slot:

Now slot sill shows AAA, both lower and upper/larger view do not show AAA.
I saw this kind of problems in patched games when trying to build submersible carrier. Some people say they can build them, I could not. I don't remember what I finally found about it.
Back to AAA transports:
You seem to have full workshop. Clean it from obsolete designs, upgrade what you can, you have over 7000 EC, a lot. Then in upatched game you could maybe build AAA transports.
If not, you could steal some from Gaians, but after you destroy/conquer Hunter-seeker Algorithm SP. built cruiser probe team or foil probe team to do it. You must though find an opportunity when AAA transport travels alone...
I haven't checked if Morgan has them.
0-<6>-5*3, that's quite effective design, in scenario editor I attacked it (PK unit now) with Gaian Shard needlejet, AAA transport survived.
That's an interesting idea for pre-defined units for scenarios.