To Intruder:
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Thanx for your post. I have updated the scenario to be more precise. Now what do you say.
Saving time & fuel is a noble quest. However, are you sure the departure airport is your only option? If not, consider another suitable alternative within your 2-hour hold time.
At what weight will your "factored" landing distance equal the runway length? Why is a 1.67 factor used in the first place? Is it used simply for additional margin for a rejected T/O, or is there some kind of landing consideration? Does it include use of reversers? Autobrakes? Full braking? Normal braking?
If your 5700' figure includes air distance from threshhold to touchdown point, and normal braking, I see no reason to wait for landing due to the runway length. If the crew is reasonably proficient, even the lack of ILS should not be a problem, especially if VASI or PAPI is available..