Hard issues here. I imagine few of us planned to become curators. We've done what we can, by our lights, to keep these fifty-somthing-year-old cars going because they are lovely to drive.
The case is not that different from fifty or so years ago, when these same cars were surviving our, or someones adolescence, and at the same time trying to ward off assault by the fleet of cars, none of whose bumpers matched ours, and few of which had adequate power-assist steering. Those were times when one routinely parallel parked on busy city streets, replaced half-a-dozen tail lights a year, and counted the creases in the front and rear fenders, despising the offenders who parked by "touch." Still, so many of these cars survived, neglected or not. And many of them stayed on the road: they were so lovely to drive.
I think, from the luxury of the keyboard, that I would have refused to have the car pushed across the lanes of traffic. But, then, I have a TR3, with only "bumperettes" at the rear. I do think some such stance might be worthwhile in these circumstances, and worth the fines, simply to insist on the point: the "Little British Cars" of the era continue to prove their value. They're still here because they are so lovely to drive. And, if they require special treatment, then that's exactly what they should get. The traffic backed up to Blaine should cope by other means.