At risk of harming my CT Personal bias, I’ve realized that it’s possible for Oswald to have arrived at 10th and Patton st as early as 1:06 pm
This timeline requires discarding Mrs Reid’s 2min post shots encounter with Oswald in the 2nd floor office and discounting McWatters bus ride as some OTHER man whom McWatters mistakenly thought might have been Oswald.
The transfer ticket may be rejected on grounds it was pristine , and had no fingerprints of Oswald or McWatters on it . It is suspect as planted evidence.
This leaves Pierce Allman reporter encounter with Oswald in the front lobby entrance of TSBD approx 2:15 sec post shots as plausible and allows Oswald to exit front entrance of TSBD by 2:30 sec before DPD officer Barnett arrived to lock the front door about 3 min post shots ( by Barnett’s estimate)
Note: Allman was able to enter TSBD before the front door was locked by Barnett, hence the 2:15 sec estimate allows a brief encounter with Oswald and Oswald still having time to exit front door preceding Barnett’s arrival at 3 min post shots.
Therefore the adjusted scenario has Oswald plausibly being seen by BW Frazier at Elm/Houston st intersection at 2:45 sec and then Frazier able to return into TSBD just before the 3min post shot mark of Officer Barnett locking the entrance door.
The WC theory has Oswald in anxious desire to return to his boarding room ASAP. Therefore it is not implausible that perhaps Oswald chose the fastest possible way, which is go directly to find a taxi.
The alternative is some vehicle driven by unknown person, Such as the rambler station wagon DC man driver story ( Roger Craig etc. sighting) . This must be discarded if William Walley’s ID of Oswald is valid.
What is left is for Oswald to have walked directly from.Elm/Houston st intersection to William Walleys taxi, Oswald arriving there approx by 12:39-12:40pm
This is consistent with Walleys Taxi manifest having recorded the pickup in the 12:30 to 12:45 section.
It’s entirely plausible that William Walley was able to drive his taxi a bit faster than his WC time trial and arrive 5 blocks from Oswalds boarding house in 7:30 sec. (The reasoning here is that during the WC time trial, Walley would be following the speed limit , as opposed while on his own, unscrutinized, probably driving a bit faster )

Thus, at approx 12:47:30 , Oswald departs Walleys taxi.
If Oswald the began a double time jog to his boarding room, 5 blocks away, he would arrive at the front door approx 12:50 pm.
Exiting at 12:55pm, Oswald then was able to have plausibly walked at fast pace the0.9 mile to 10th and Patton in 11 minutes, arriving there at 1:06 pm