Simple, dont get so fast you loose elevator control. Normally, i would zero the throtle and dive using the rudder to skid the aircraft on the way down (use some aileron to correct the secondary effect of the rudder). If you find you are still loosing elevator control, then a shallower dive is called for. If you do get loss of elev control, sometimes up elev trim can help recovery - i doesn't work miracles tho...
BTW, its not actually compressing, its just getting extremely heavy. Compression happens as you approach the speed of sound, 109 elev stiffness happens somewhat earlier than mach 1.