I recall a discussion where, unless more than a few minutes has lapsed in between texts, the phone will not display a time stamp for each. It assumes a "conversation" is going on. With more than a few minutes delay (see the 15 min delay between 745 and 801 as an example, a new time stamp will appear. For this reason, II assume that last flurry of texts happened all very close to 8:01 and was over by 8:05 at the latest.
Going by that, DR must have told him he couldn't go that night by 6:45 or so.