Hi Mike,
Thank you very much for checking this out for me; I have finally got to the bottom of the issue.
I had to recreate my "Domains" package group and all the LogicBoxes packages. Naturally, I then had to re-add the newly created "working" LogicBoxes' packages to my clients. Now that I have done all of this, the order form works correctly and the LogicBoxes orderids have been fetched, so now the domain details are showing (they weren't before). Fingers crossed that this will also mean that the domains will now start to auto-renew as well! Thanks!