There is another way, which I can think of, albeit just slightly more risky.
Melt one of your ships you intend to keep. Buy the Carrack.
Then lodge a support ticket, and ask if they would be so kind as to unmelt your ship. Offer to buy some things from the store to put enough credit in there.
They are very likely to unmelt it, though there is nothing that requires them to. I would rate your odds at 90%
Just giving you all the options.