The pilot's manual describes the level flight maximum altitude. The zoom climb scenario you describe is certainly possible but it'd be a pretty risky maneuver. First of all, the SR-71 wasn't a very strong airplane. Things start to break pretty quickly if you pull more than a couple Gs. You'd also risk stalling the airplane because your speed would quickly decay below the minimum KEAS value for any given altitude.

Second, after the engines quit, you'd have to descend quite a bit before you could ignite them again. That would make you pretty vulnerable to another volley of SAMs. I'll ask my coworker (the one who was an RSO for 5 years) if that is a reasonable scenario.

From what I've read, the Blackbird was the first modern stealth aircraft (the WWII British Mosquito was probably the first since it was made out of wood). Between a low RCS value, high altitude, and high speed, they were probably able to avoid SAMs simply because by the time they were detected, it would've been too late to get a radar lock and fire the missiles. Even a SAM takes a while to reach 85,000 feet. With the Blackbird moving a mile in less than 2 seconds, it might've just been too fast to intercept. In addition, they would've made it a point to plan their missions to stay as far as possible from known missile sites, just as the modern stealth aircraft do.