But it's very possible that Markham was just approximating (i.e., rounding off) the time when she said "1:15". A lot of people do such "rounding off". Don't you?
When people are asked "What time is it?" and it's 1:12, a common response would be, "It's just about a quarter after."
Desperation of full display!
Let's complicate matters a bit further for you. Markham and Bowley are inseparably linked together by the times they arrived at the scene. Markham arrived about 1 minute before the shooting and saw a man crossing Patton walking east being followed by a patrol car. Bowley arrived no more than about 1 minute after the shooting. We know this because Callaway was on the scene within less than 3 minutes after the shots and by then Bowley had already made his 48 seconds long radio call.
Markham and Bowley's actions can be traced and timed. Markham left her home at 1:06 or 1:07 and only needed to walk one block of 400 feet to get to 10th and Patton, which would have taken her 3 minutes. Bowley picked up his daughter from school at 12:55 and only needed to drive 6.3 miles or about 13 to 15 minutes to arrive at 10th and Patton.
If you push Markham's timing further back, as you've tried to do, by nearly 5 minutes, you need to do the same for Bowley and the other way around. The only time that really makes sense for Markham and Bowley to both be at the scene is if Tippit was killed between 1:09 and 1:11 at the latest. But maybe that's just to much rationality for you.