Wiz. Here's another way to consider it. Newton and F=ma.
You've said true airspeed will be increasing. Thus aircraft is accellerating. thus unbalanced force on the aircraft. And simply since the case is going straight up, the up force greater than the down force. thus Thrust greater than weight plus drag. Thus if thrust equals weight plus drag, aircraft cannot maintain same ias.
'm with Hawk on this on
Stan