Other than steadily working through all the available ports, I can't think of any obvious way to test for a faulty line-card.
From what I recall, they don't all fail at the same time which is what made it harder to find.
I don't have all the details as it was Azzaka who was speaking to Openreach about it... and its several years ago now. All I do know is that when the fault presents it looked remarkably REIN like on Routerstats/DSLstats. Unfortunately Azzaka no longer works at Zen so isnt around to ask.
It is something to bear in mind that if a line is displaying unattributable REIN like symptoms, then the port could be faulty.
Please bear in mind I may be giving you a red herring by mentioning a faulty line card, but with you having had port swaps which have also gone bad it does sound a bit suspect.
I wonder if you can get a Lift and Shift to another Line card (not port) on the MSAN. I wouldn't even know how to approach TT with that, as I think port swaps are usually initiated by the Openreach engineer suspecting a bad port. Problem is with you being with TT, unlike with BTw then the request goes back to the SP.
I would think the best course of action would be explaining to the Openreach engineer that you are now on your 4th port which fails after a certain period... and if he thinks it could be the line card rather than port.