I'd advise you have a look at the MiG-31D and S variants which are pretty similar to what you're getting at.
In my experience I'd be skeptical that you can zoom climb from M2.0/60kft to M0.8/110kft.
Looking at the equation for energy height:
V1^2/2g + H1 = V2^2/2g + H2
M2.1/60,000ft gives a starting energy of 37823. A quick look at zero speed means that you should be able to zoom climb to ~124,000ft, however in practise it'll be less than that due to energy spent in the pull up and aerodynamic drag. Doing the calculations for 110,000ft and you can theoretically get to ~M0.98 as a maximum, but again this is discounting drag.
It's probably worth having a look at the NF-104 as well. With a similar zoom climb profile, but having a rocket engine to continue supplying thrust during ascent, those flights were maxing out at 110-120,000ft.
I think my general point is that it's probably worthwhile re-checking your performance calculations.