Insulating/preventing heat transfer on non-IC rated recessed lights
Air Tight recessed lights might prevent air seepage from a conditioned area to a non-conditioned area, but they can't do much about thermal transfer.

Proper insulation is the only way to fix large amount of thermal leakage. However, your predicament is going to be that your fixtures are not insulation-contact (IC) rated.

With non-IC fixtures, you'll not only find 


  Do not install insulation within 3" of fixture


But you'll likely also find


  Nor above fixture in such a manner to entrap heat


Example



You'll need to check the warning labels and/or instructions for your particular lights, but this all but eliminates the option of putting some sort of heat-trapping box above a fixture with such warning.

You will find it difficult to find a 4" IC rated remodel fixture. They just aren't readily available on the market, except for some speciality LED-driven models.