Hello, I would check for any vacuum issues at the engine. A correlation of braking with engine speed is that you use a vacuum operated power brake booster to assist in braking, and you are manipulating that vacuum with your foot on the brake. The engine is producing this vacuum, and if there is some kind of vacuum leak or issue this can cause the idle to fluctuate. However, this should be something any good technician and shop can duplicate, so I'm uncertain why it can't be resolved, or hasn't been able to be resolved, to date.
This is just a guess of course; hands on testing is needed, especially with test equipment. I would expect fuel trims and air / fuel ratios would fluctuate if monitored while the concern is happening too as a result.
Keep in mind: This assumes a gasoline engine and a vacuum operated brake booster. You did not list engine size or type, so it is only a guess.
Engine rpm increasing to 1,000 at stop light should not present a problem with keeping vehicle from creeping - with ‘normal’ service brake application.
This could be due to an accessory turning on - such as the A/C compressor as it too is operational in cold temperatures when certain hvac settings are selected.
Perhaps the technician at the “Chevrolet garage” is simply applying the service brake as it should be... *perhaps*
GMC 2500 likely equipped with Hydo-Boost brake system.