Ok this works very nicely, and I got it to work both cross realm and same realm. Earlier I tried it with someone on the same realm, but that failed at first until we realized the next day the transmog reappeared, whereas on cross realm it worked straight away.
Basically you need to relog after receiving the items from the trade.
And for proof, here's a warlock with tier 3 priest:
https://i.imgur.com/d2jT7.jpg
Attachment 7199
This ends up working because tier 3 has no class restrictions (probably due to the fact it was a quest reward and not a drop), and the person that wants the transmog has to be able to equip the source of the transmog.
Here is the process:
1) Repeatedly doing lowbie instances with me needing the cloth gear to obtain all the different slots, including a staff
2) I'd equip the lowbie gear (blue/epic BoPs)
3) Transmogrify it to t3
4) Open trade with friend who was there when I looted the items. I never unequipped the items. I simply opened trade by right clicking their unit frame, then dragging it straight from my character slow into the trade window.
5) He accepts items
6) He relogs
7) Win
Worked 100% of the time, as long as he is able to equip the transmog source (in this case it was Faith T3). Sadly this means that a Benediction/Anathema transmog cannot be traded to non-priests.