Most Ti frames are going to be super comfortable, but if you find the Specialized too flexy, you may have issues with a ti bike as well. I'm 175 lbs and I notice flex in my Moots when climbing anything over 8%.

What is your saddle to bar drop on your current bike? "somewhere between an aggresive position to more relax" is extremely subjective. Also, what wheels are you running? Sometimes that perceived frame flex is in the wheels, so if you're happy with the fit on your current bike it may be worth trying to demo a stiffer wheelset.