Nobody said continue to MDH/DH, just there's no screaming rush for the go-around. A couple of hundred feet just to re-iterate the procedure isn't going to cause anyone a problem.
Chatting for a few seconds and initiating at 1000' instead of 1500' isn't going to cause your mate with the broken nosewheel any problems but it is likely to be a much more relaxed manoeuvre for you.
CAT III approaches have their own problems and the brief will have alluded to them for the events you listed. RVR's are advisory below 1000' so continue anyway if below or a nice gentle go-around if above. I've always found CAT IIIB No DH in 75m RVR an interesting prospect anyway and a mandatory go-around below critical altitude has to be immediate. You will find in my previous posts that actions AT decision height/alt have to be immediate. Again early in the approach what's the rush? As you get down to the limits then there is a need for immediate action, I would counter that the further back up the slope you are the necessity for 'immediate' (and rushed) action reduces.
Keep it simple.