Do you refuse to leave TPA until on base in similar circumstances when operating under VFR? If not, I don't see the point of delaying the descent and potentially causing yourself to be unable to descend to the runway in a low-vis situation, forcing yourself into a missed approach from below MDA (a bad corner to be in). Remember, you're training your students to fly all sorts of planes at all sorts of airports, not just a 172 at the home 'drome.
Of course not -- but standard TPA is 1000' AGL, with variations from 800-1200' AGL.
Most Circling approach MDAs range from 600 to 1000' AGL.
If I'm 600' AGL on a circling downwind, why descend before being established on final?
If I'm 1000' AGL on downwind, and out of the clouds and the runway is in sight, then it's a VFR landing, with normal pattern procedures.
That said -- of all the airports I've flown to in the past year with IMC and real approach required -- all have been served by an IAP that precluded the need for circling, and the few times I've had to circle, I've used the IAP to get "in the pattern", canceled VFR, and landed using normal VFR pattern procedures.
While I think it's important to consider all the possible options/conditions/situations, I just haven't had the need to do a CTL at MDA minimums -- the complete list of circumstances simply hasn't presented itself yet -- at home or away -- but we all do far more approaches at home than we do away.
One local airport I use has only one IAP , but when the weather's so poor that a LOC 5 is required, the winds will
almost always permit a straight in. Given the nearby ridge and obstructions, it's simply not in my playbook to CTL at that airport at minimums -- and I know it pretty well.
Discretion is the better part of valor and I would fly the extra 10-20 miles and land an airport with more options.