WOW!! Reading about the Foxbat and writing fiction and knowing about the Foxbat and then writing per expertise are two different things, I hope you get that. You should talk to the fine USAF pilots who took out a few Foxbats in Iraq and other places. Then you'll find out how Foxbat really flies at Mach 2.4 at 70k feet.
At 65+ feet, maneuvering gets very difficult due to the gravity and air-density, etc. If you can install a bigger engine into the F-16 and take it up there, it's maneuverability would become less than 50% of what it really is below 55K feet. At the height of 70k or more, you can't do "maneuvers" and still maintain a 2.5 mach speed. You make one turn and you bleed so much energy that it takes you a couple of minutes to recoup and due to gravity and drag, you become a sitting duck.
A Foxbat, a U-2 or a SR-71, are only at their peak performance if they cut through the air like a needle, meaning straight flight. No maneuvers at that altitude. An F-16 if fires a couple of AIM's, and the Foxbat pilot does a roll or two, or some small maneuver, his speed will drastically reduce and the vector will change (all Physics here, every motion has an equal and opposite reaction). So a vector change will bring down the original vector flight pattern from a speed, gravity and drag's standpoint as the third law of motion will kick in.
That gives both, the F-16 and the AIM more time to now get closer to the Foxbat. It would take a minute to two for the Foxbat to recover and become a vector again. But a Mach 2.5-3 missile having a much smaller body will get closer to the Foxbat in the meantime, forcing the jet to do more maneuvers and thus a second missile would take advantage of that slower speed and bleeding energy and would more than likely take him out. Hope this helps.
I just explained this, hopefully this answer will become a part of the previous post so you can read it. The reason as to why no SR's were intercepted was because the US had provided a strict vector based flight pattern for the SR's. They weren't allowed to engage or maneuver. Their goal was to penetrate any AD and fly like a needle through any airspace. As long as this jet would fly as a Vector, it would be extremely hard (if not impossible with tech from back then) to intercept it.
Before anyone can get to them, there would be support waiting in the shape of F-14's, F-15's and in earlier times, F-4's.