I'm asking myself how much comfort do you give away for a little extra speed?
Comfort is speed.
Your body can absorb significant amounts of energy* when being rattled about by rough roads or by an over-stiff bike, and your legs have to supply it.
With quality tyres, you don't lose much in terms of pure rolling resistance (i.e. hysteresis in flexing the sidewalls) at lower pressures, and can easily gain more than you lose.
For an important one-off ride like TCR, I'd look at Compass Stampede Pass (32 mm) or Compass Bon Jon (35 mm), depending on clearance, and run them at a pressure aimed for best comfort without risking snakebites. (from Velo Vitality, in the UK).
Hard tyres tend to feel faster even if they aren't - compare times for similar rides instead of going by feel, and average over enough rides yo cancel out weather changes etc.
*deliberate selection of a very poor surface has shown an extra 290 watts to maintain 26 km/h, compared with a smooth road