The only thing I can think you're basing that time on is the testimony of Earlene Roberts in which she says:
Now, it must have been around 1 o'clock, or maybe a little after..."
Indeed, but it needs to be placed in context. She said that she was trying to get the television to work so she could watch the 1 PM news to find out more about Kennedy.
Also, the evidence presented by the WC about Oswald's journey from the TSBD to the rooming house does not leave much room for him to have arrived prior to 1 PM.
And you also need to take in account that the fastest way on foot from the rooming house to 10th street takes 11 minutes, according to a split time trial Gary Mack did some years ago. Personally I'm not convinced of that time, because I am a fast walker and when I walked the distance it took me 12,5 minutes.
If Tippit was shot at 1:09, then Oswald must have been there at least a minute earlier, which means 1:08. Obviously that would mean that he left the rooming house at around 12:56 which, IMO, is impossible.
Impossible??
If the shooting happens at exactly 1:09 PM
And
If Oswald arrives exactly one minute beforehand at 1:08 PM
And
if Mack's time of 11 minutes is correct.
This has Oswald leaving the house at 12:57 PM.
Is that also impossible?
What if the shooting happens at 1:09.30 PM
What if Bowley's watch reads 1: 10.30 PM
And
what if Oswald only needs to be there 30 seconds beforehand, at 1:09 PM
This has Oswald leaving the house at 12:58 PM.
Is that impossible?
"Indeed, but it needs to be placed in context. She said that she was trying to get the television to work so she could watch the 1 PM news to find out more about Kennedy."I'm not familiar with this statement bit it doesn't seem to exclude the possibility that she was trying to get it to work
before the 1:00 PM news.
"Also, the evidence presented by the WC about Oswald's journey from the TSBD to the rooming house does not leave much room for him to have arrived prior to 1 PM."But it does leave some time. How much time does it leave - 2 minutes, 3 minutes, 4 minutes. 5 minutes? What is the exact time Oswald gets in the taxi? What is the exact amount of time taken for the taxi ride? How quickly does Oswald move to cover the distance back to the rooming house from where the taxi drops him off? How long is he in his room?
These things can't be known with exact precision, hence the need for a range of times.
I most certainly do not accept that it is "impossible" for Oswald to be around 10th and Patton for the timeline you are presenting.