The Premises of Traveller: 1. "Jump takes a week/No ansibles"

Just like Leviathan had "Jump torpedoes" that had to be explicitly nixxed subsequently. Sometimes stuff slips past the editors.
In LBB1 77 it was a jump capable 50kg missile.

I still sort of like the idea of "sub-volume" jump devices like jump torpedoes. I believe TNE used ~ 50ton "Jump-Boats" in the Regency as part of its "X-Web" system, and simply noted that they had a significant risk of mis-jump and suffered high loss rates. That might be the simplest (and a believable) solution to the issue.
Re. an ansible at very high TL, I totally agree and have this in my setting (tachyon communication). In general, fantastic tech in NPCs and sporadically available to the PCs is also good, so long as it is hard to hold on to.