FWIW, the riding you describe doesn't sound like you need a TT bike.

Of course, everyone is free to ride what they like but, TT bikes are specialised bits of kit , not really designed for general cycling. There are plenty of loons ( self included) who ride them all the time cause we lovethem/need the practice/can'tafford2bikes.....but they are still specialised and that means compromises. Maybe you're better off on a good road bike and just add some aero bars if you want to use that position from time to time. Focus on good fit & the issues you face will go away. If you buy a TT bike, you'll still need to get it fitted - maybe even more so.

best of luck.