You are missing the point chaps. You physically cannot fly the original missed approach (at LHR at least). You must detune the original ILS to turn towards the other runway otherwise the flight recorder will throw up a deviation and an unstabilised approach. Therefore come a GA, you would have to retune the ILS to check DME readings for a GA, in the middle of a GA, and commence your turn very rapidly.
Besides which BA issued a notice to decline such swingovers about 4 or 5 years ago, for this very reason.
I'm afraid this is very academic now- it is no longer a simple procedure as it used to be before flight recorder monitoring. I shall certainly decline it unless it is understood the procedure to follow, but that is not easy when LHR tower is so congested sometimes you cannot break in to say anything. It's asking for an incident. Nowadays we are supposed to be stabilised with no turns by 1000'. It can no longer be done.
I'm afraid it is no longer thought through. If you are switched runways 12 miles out? Are people suggesting you fly the original runway GA? That's daft. So where is the 'dividing line' where ATC will expect you to fly the new GA or the old one? Where does it become a 'changed' approach and not a runway swingover? If I'm 15 miles out from AMS 27 and they switch me to 24, will they really expect me to fly a 27 GA? I bet it would cause considerable surprise! It's important because line pilots just do not have this information- and they are the ones that count, not some ATC rule book!.