I understand you to be saying that (1) there is an interference pattern being displayed (at least if there's an ordinary screen) AND (2) there is the ability to determine time-of-flight accurately enough to distinguish slit identity.
Now, (2) is possible only if the source is pulsed more briefly than the difference in time-of-flights. But, as I showed quantitatively, and then Henning showed in a nice verbal display (at his paragraph 4), this makes (1) impossible.
But I'm beginning to see that for you, and some others, the question has to do with something about detectors and knowledge.
The answer to that question is trivial -- there is no effect. Knowledge has nothing to do with loss of coherence/interference. It isn't an issue of the precise time-of-flight being known, but being in principle knowable.the difference to ponder here is the effect of knowing the slit identity.
The nicest illustration of this that I've seen is in some experiments from Mandel, particularly Zou, Wang, and Mandel PRL 67, 318 (1991). Here, two coherently pumped downconversion crystals send their signal photons on the two arms of an interferometer, with the correlated idler photons leaving the apparatus on defined paths. If an idler photon were detected, it would tell which interferometer arm (path) were taken, hence no interference. But in this experiment the idler photons are not detected. If they are directed by reflections to leave on the same path, there is interference of the signal photons in the interferometer. If the idlers leave on divergent paths, there is no such interference. In neither case is there detection of the idlers. It has nothing to do with "knowing" anything; rather, it is entirely a matter of there being a distinguishing difference somewhere in the universe. (I hope it's obvious that, if the idler photons leave on the same path, the detection of a photon on that path gives no signal path information, because they can not be labeled "idler 1" and "idler 2".)
Of course, given such a distinguishing difference, an experimenter might measure it, and then know. But that is entirely a secondary, derivative result, not the "cause" of the loss of interference.
Relating this to the current question, then: The nature of the detecting screen, whether a photographic film integrating over time, or a video screen giving many instantaneous records, has no effect whatsoever on the existence of an interference pattern.
Turning now to the issue of numbers. (I've been a physicist for more than fifty years, and I believe I've never seen such resistance from physicists to dealing with physical reality. Gedankenexperimenten are not arbitrary fantasies; if you want to violate fundamental laws, you need to propose that up front.)
If we place the detector at the first minimum, we must pulse the source into a packet less than a half-wavelength long. The will create such a broadband signal that there will be no interference pattern possible, regardless of distinguishability issues. So instead let's place the detector at the 10th minimum, so the distinguishing pulse can be as much as 8 or 9 wavelengths long. This isn't monochromatic by any means, but it would allow a fuzzy pattern to exist. In this case, we have an interference pattern in the center, becoming less and less sharp as we go out, and vanishing by the 10th minimum, as the temporal overlap of the waves at the screen becomes less and less.
So we see that if you don't consider numbers at all, you could be dealing with a trivialized situation -- everything is smeared out. And if you do think a bit quantitatively, you come up with interesting results like this -- the gradual vanishing of the interference pattern with distance from the central axis.
Finally, wavefunction, your last post (appearing just as I'm finishing this) is correct. That it is possible to distinguish the paths is everything; whether anyone has bothered to do so is irrelevant. So I don't understand why you seem to treat this issue of knowledge in the opposite fashion in your immediately previous post.