I'm working from home at the moment, like a lot of people. As today was quiter and not as busy I decided to try and test the games taxi services in the background while I was working (I wouldn't be able to pilot my ship as I might have to answer calls and such). I had a transport mission from station A. I used Apex's taxi services to go to station B, then when I was there used Inter-Astra to bring my ship over also. So far so good. Once my ship arrived I went into the hanger and used the market to fill up my ships cargo hold with the required item. I then disembarked, went back to the taxi hub and got an Apex taxi back over to Station A. Once in station A i used Inter-Astra to transport my ship back over. Unfortunately Inter-Astra decided to loot my entire cargo bay without warning!
I honestly didn't think it would work, but I just assumed it wouldn't let you transport the ship, I didn't think they would just empty your cargo. I imagine this is to deter people using this method to avoid pirates and interdictions but a warning would have been nice. So heads up, this method doesn't work….