In the 70's, Dallas Morning News reporter Earl Golz interviewed a nurse named Thompson, who was one of the Methodist ER staff attending to Tippit that afternoon. She said that the Methodist ER clock was off by 15 minutes that day. Dale Myers interviewed Dr Mohlenhoff, who assisted Dr Liguori's attempt to resuscitate Tippit. Mohlenhoff said that any timing discrepancy would have been due to issues with the Methodist time system. Therefore, your attempt to build a case around Methodist time will fail miserably, since you're relying on the least realiable clock that day.
And James Bowles said:
1. No exact record of "time" exists
2. The several clocks were not synchronized
3. The radio operators were not exact with regard to "time statements" on either radio
So there is no basis whatever to gauge the relative reliability of any of the various time claims.
Beside, this is all moot anyway, given that there is no way to determine how much time elapsed between the actual shooting and the "hello police operator call", even if you could accurately pinpoint when that happened.