2004 4l80e hot trans on hills

Hey this sounds too familiar... have a k3500 2004 had the same exact issue. First off and trust me on this. Are the brake lines rusted? If so have them replace along with the booster pump on the front of the engine and the steel coolant lines. For the first year or so i owned the truck engine/tranny temp kept climbing on 6% grades it would red line on really hot days. (See my posts) changed the fan clutch, belts, hoses, waterpump, all help but still same issue. We were up in ossippee, nh 2hrs from home heard a high pitch whine then it stopped as we crested the hill, engine temp and tranny temp all went normal. going down steering felt weird so i tapped the break right to the floor used trailer breaks to stop at a truck pullout near mcdonalds. garage replaced the booster pump which supplies fluid for steering, and brakes. A piece of rust jammed it up and cause it to stop cooling which took away coolant from the tranny and engine. the coolant was too hot. A week later relocating the trailer the brake lines let go stopped with trailer breaks again $600 for the booster pump $635 for new break lines.