There have been HPR rockets with active guidance using gimbaled motor mounts. Some of the photos show a "lot" of deflection from the motor to straighten the flight out.
Not just HPR... John Pursley has flown several "large mod-rocs" at NARAM's, including the finless Vanguard, a scale finned Redstone, and (IIRC) a Saturn V all with active guidance from model airplane autopilot devices (for the 'brains' of the system, using it's horizon sensors feeding into the device which sends control signals to a pair of servos in the gimballed engine mount for thrust vector control (TVC in NASA parlance), all of which were powered by "G" size motors, utilizing super-lightweight construction, which kept them in the "model rocket" category, not HPR territory...
Just sayin'....
It IS possible to do on large model rockets and stay under the HPR limits...
Later! OL JR
PS. There is also ANOTHER form of TVC that was used on the Titan III/IV rockets and all the US solid fuelled submarine launched ballistic missiles, or SLBM's. This system uses a 'steering fluid' which is injected into the rocket nozzle to divert the rocket exhaust coming out of the nozzle to create steering forces. The system uses an arrangement of a series of injectors and valves arranged in a ring around the nozzle, and a tank of "steering fluid" (hydrazine IIRC) in the base of the rocket. The guidance system of the rocket senses the rocket's orientation and flight direction and any deviations from the desired flight path, and near-instantly determines the corrective actions needed, and activates the proper valve(s) on the rocket nozzle to inject the steering fluid into the nozzle on the side opposite the direction the exhaust needs to be diverted, which then causes the rocket exhaust to point 'away' from the injector, steering the rocket back on course. This system was developed for the Polaris missile, because it was MUCH more compact than a standard gimbal-nozzle TVC system used on other solid fuelled land based ICBM's like Minuteman, and space was the ABSOLUTE confining factor inside a submarine! The follow on missiles after Polaris, Poseidon and Trident, have used the same system IIRC.
Titan III/IV used the same system in it's SRB's, coupled with a non-swivelling nozzle, to achieve TVC control during the SRB burn, often coupled with the Titan's core liquid fuelled engines being airlit near SRB burnout. Kinda cool!
OL JR