I for one shall stick my neck out and say if you have been cleared for an instrument procedure on 27L and then lose the runway whilst trying to circle for 27R, then my 0.02p's worth is that you fly the missed approach procedure for the runway that you initially shot the approach on.
People above have mentioned parallel runways, thats a bit of a red herring.
Luckily circling is not something we do often. But consider 27ILS at Memphis circle for the 18's and perhaps a bit more nearer home 27ILS and circle R22 at Amsterjam, doing the 22 go around would cause chaos!
Now between the 0 degree difference in runway heading in the case of a parallel runway and the 90degree difference at Memphis is there a certain difference of alignment that we should change procedure?