As you're aware, 23" was a pretty standard "tall" size for production bikes during the golden age of club cycling, so I'm making the best of it!
Being tall and not getting the correct period fit w/ barely a "fist" of seatpost showing at most as seen in the flic or a "french fit" on the small-ish standard sized Brit production frames of the era will most certainly affect both comfort and handling. Sorry to say but investing a lot of time, effort and $ into a frame-set that just does not fit is a waste of all whether it's a 50's Brit club machine or a modern state of the current art TT bike.
25" frames became much more common in the late 60's with a host of geometry, drive-train and component changes from Brit mfgs. Perhaps not your period of interest but doing a backwards downgrade on components on a tall late 60's 531 club bike would be rideable in both fit and operating experience. I won't tell the Period Correct Police if you don't.
-Bandera