I don’t know anything which will reduce static and dynamic pressure of cold which is the problem. A NRV might block it, but likely as not there won’t be enough head from the loft tank in the hot line to operate a NRV in the forward direction. – By your admission, the reverse static pressure is bigger then the forward, so how will the NRV ever open? Even if it does, you might then get a very measly amount of hot in the mix, and it might not give you a a hot shower. If the cold is flowing back up the hot with the mixer turned off now, I’m fairly surprised you can actually have a hot shower at all.
The only proper way is to reconnect the cold from the loft header tank. Ideally it should have an independent feed from the tank to prevent pressure changes when someone turns on a tap elsewhere.
There is one shower brand I’ve seen that was a cold mains “powered” – effectively a power shower. Can’t recall the brand, but it uses cold mains water pressure as the energy source to pump the hot. The outcome is cold water “waste” at low pressure which you’d need to put into the drain.