I repeat- we are not talking circling approaches! ATC have switched you to another runway. They will then expect you to follow procedures for that runway. If following the original runway's GA leads to a hazard (as at LHR) then you will cause considerable surprise in the tower following a procedure that is not expected by ATC. It is 10 years since I have habitually visited FRA and ZRH, I am not that familiar with them anymore.
Does the logic some of you are using mean that if at 3000' I am switched over to another runway, then I should fly the original GA? Extraordinary!