I have to say, Martin, that I'm coming round to your way of thinking.
602 is around 510 East Jefferson when they ask the address. Once they get 501 East 10th they only have to drive a short distance up Denver to the intersection with 10th. When they get to the intersection they only have to look left to see where the small crowd is gathered near the squad car and the call "Code 6" can go in immediately. By the time they roll up to the scene and check out the condition of Tippit, maybe open the back doors etc. there is very little time, a matter of a few seconds, in which Callaway can help load Tippit into the ambulance.
I concede that it is far more likely the sirens on Callaway's call are 602 arriving. As far as the 6 minute discrepancy is concerned...
...in one set of scales is a preponderance of interlocking testimony in the other the 6 minute discrepancy.
Having the ambulance arrive before Callaway's call on the DPD tapes threw me and I hadn't appreciated the very small amount in time which Callaway would have to help out loading Tippit.
Shots at 1:09 PM
So, you're a truth seeker after all. Well done!

One final comment about the DPD radio transcripts, going by what Bowles told the HSCA;
Let's say the real time is
1:10But the master clock connected to the City Hall system shows
1:12 as "official" time
And the clocks used by the dispatchers are all different and 2 minutes faster than the "official" time. That gets the time up to
1:14.And then consider that the dispatchers were not always punctual in giving the correct time stamp, so consider an error rate of 2 minutes and you can end up with a time stamp of
1:16 when the real time is actually
1:10.Once the error of a wrong time stamp crept in it was unlikely to be corrected as long as the dispatchers were busy.
I fully appreciate that this may be hard for some to believe or accept, but, considering what Bowles said, it clearly is a possibility that this is what happened and even more so when one considers the fact that it must have been pandemonium at the dispatchers office just after Kennedy's and Tippit's murder. Phone calls coming in, "call sheets" coming in on a conveyer belt and constant radio calls. I can imagine that under those hectic circumstances a dispatcher might lose sight of the time.
Now comes IMO the more difficult part. Can it be determined that the time stamps on DPD radio tapes were simply off because of the problems with the system as described above or are there possibly indications that the actual recordings (made on voice activated equipment) were manipulated.