In the USAF, the jet I flew was a Cat D aircraft, however we flew many circling approaches as well as circling No-Flap approaches. When flying a No-Flap approach, if our approach speed exceeded 165 Knots which mandated we use the CAT E minimums on the approach plate. So even though we were a CAT D aircraft we changed our category depending on our approach speed for the maneuver being flown.
As far as missed approaches and the 2.5 degree climb gradient, my airline has “special engine out” procedures for airports whose terrain will not support a “straight out “ missed approach procedure flown at a 2.5 degree climb gradient. In these cases a special engine out procedure is designed to avoid terrain in an engine out scenario. Also we are required in the event of an engine out approach to check our engine out climb gradient. If the gradient exceeds the minimum required for the normal missed approach procedure we can fly the MAP as published on the approach plate. However, if the min climb gradient, engine out, is less than the published MAP procedure ( based on all engines operating) then we have to fly the special engine out procedure in lieu of the published missed approach procedure. We are further required to let ATC know our intentions, as we are told that ATC may not know what our company designed Special eng out procedure is.