I'm not sure where your found the 4-7 hours submerged time, it may be applicable for some species of sea turtles, but I don't believe the Hawksbill can stay under water for anywhere near that length of time, especially while under duress.
I believe it was Sea World Orlando that published data stating that the Hawksbill can remain underwater less than an hour.
BTW, I strongly encourage the tagging program. I hope some valid science is obtained from it.
I did provide the the link in my original response, however I should have included the text since there are some variances in the time...
"A resting/sleeping turtle can remain underwater for over 4-7 hours. Recent research has shown that some turtles can even hibernate in the sea for several months! However, a stressed turtle, for instance entangled in fishing gear, quickly uses up oxygen stored within its body and may drown within minutes through panic.
I assumed that, anyone doing this for research would do their best to coax the turtle and not drag or ride him to the surface. They obviously didn't drown so, its all good.