Folks,
I can vouch for the Mach tuck characteristics of a B707, it could be hard enough that the nose down pitch exceeded the authority of the elevator, and with that elevator load the stab trim motors would stall out. The only successful recovery was to split the spoilers and pull the speedbrakes. The USAF lost at least on KC-135 like this, several civil 707's were lost.
It didn't need to be a -120/138 or -720, the -300 and -320 were no better.
Having said all that, the aerodynamics that cause tuck are well known, unless there is something weird about the Avanti wing (and I don't think there is) M0.70 (or M0.77) would not be fast enough to have an area of pressure shift in transonic flow to produce the centre of lift change that is tuck.
Tootle pip!!