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Haha I don't think its either of those. I think its literally sloshing at those speed/acceleration and going out of balance. Increasing speed more gradual upto xxx it behaves normally.
The real fix is going to be refurb all the wheels, but means a trip to Yorkshire (5 hours each way), and TBH don't have time. None of the wheel refurb spots near me appear to be able to operate basic tools like tyre levers/tyre machine without breaking everything, everytime.
BrickMan-
The body shop I work for take our wheels to a local tyre shop. They remove the tyres and then the wheels are sent elsewhere for refurb. It's a bit time consuming but the results are always good. We used to use a local (Reading) wheel refurb place but I think Stevie Wonder works there now. So perhaps go to a slightly less local tyre fitter and ask who they would use rather than if they do it themselves. I am not a wheel refurb expert either.
Constable_Savage
Ask the tyre shop to check the balancing on the offending tyre(s) as they appear to have caused an issue. It may just be that the tyres have to warm up properly to spread the sealant around the inside of the tyre. It may have pooled in what was the bottom of the tyres and due to the cold weather is reluctant to disperse. I am not a tyre expert.