If Tippit was killed at around 1:09 and Oswald was still at the rooming house at 1:03 there wouldn't have been enough time for him to get to 10th street on foot.
Right, I thought you were talking about personal consequences [my bad]
Agreed that it is unrealistic for Oswald to run 0.9 miles in 6 minutes to get there but there is no evidence, literally zero, that he left the rooming house at 1:03 PM
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..."This would seem to suggest a time around 1:03 PM taken in tandem with her observation that Oswald was in his room for "3 or 4 minutes".
However, when she qualifies why she believes it is "a little later" than 1 o'clock it is revealed she only has a vague grasp of what time it is:
" Now, it must have been around 1 o'clock, or maybe a little after,
because it was after President Kennedy had been shot-what time I wouldn't want to say..." She believes it's 1:00 PM because it's after JFK was shot!
Not because she saw it on a watch or a clock or heard it on the TV.
She actually says "what time I wouldn't want to say".
She is clearly guessing at the time and using the shooting of JFK to gauge this estimation.
To stick a specific time on this is unrealistic (IMO)
The best we can hope to do is give it a realistic range of times for when Oswald leaves the house.
It's not a question of undermining the reliability of Roberts' testimony, it's just accepting that she reveals her uncertainty regarding the time in what she says. Her uncertainty regarding his shirt is also revealed.
Conversely, she is absolutely certain about a couple of aspects of this interaction:
1) That Oswald was in a big hurry
2) That he was wearing a zip-up jacket when he left the house
As far as I'm concerned, a reasonable interpretation of Roberts' testimony reveals these two things.
A reasonable interpretation of her testimony does not allow to put a specific time on when Oswald left the rooming house.