And your last sentence basically illuminates my concerns. Talos is built for a flight OUT to a target at high straightline speed on a relatively horizontal flightpath, followed by a brief period of engagement. Some of that last stretch is going to be in coast phase, but the thing is already doing M3.2 or thereabouts at engine burnout and has some energy to spare in thin air. A flight up is another matter - is there going to be enough retained energy for manoeuvre to final engagement if the missile is coasting the last few thousand feet, with practically all the lift needed to be provided by thrust?
Methinks you'd need (as I suggested) a more powerful booster for the first phase, altering the ramjet and tweaking the fuel flow for a later start and a final phase in more rarefied air, possibly changes to the fins which changes the aerodynamic responses and the manoeuvre transfer functions, which requires changes to the electronics, etc. etc. By the time you've finished, is it really still a Talos and would the redesign effort not be better off getting put into a new missile?
I'll give you this: as a stopgap or last resort, it's almost certainly better than nothing.