First - now that I've had a chance to crunch the numbers below I see I was wrong about how fast a missile at 0.8c would pass through a formation; it'd be more than 3 seconds.
Second - due to length I've omitted any quoting of the previous post(s).
Let's set up a situation ludicrously in favor of prolonging the time a missile is within your proposed +/- 250,000 km.
[1]Give the enemy 600 gees of acceleration (something only the GA currently has), then let them start next to to missile launch site yet have an entire hour running directly away from it before it launching (which would never happen). Doing so gives them a combination of large base velocity away from the missiles (chase scenario)
and keeps the missile range down so they can't work up to their full terminal velocity.
So, we've given them more acceleration that we'd expect, put them where our missiles have lower velocity than we'd expect, and given them a much larger velocity away from us that we'd ever expect.
After that 1 hour at 600 gees the enemy is 38,102,400 km away, moving at 21,168 kps (0.07c). The missiles (Mk23s - 180s @ 46,000g per drive) will catch them 461 seconds later at a range of 47,923,329 km. The missiles' velocity is up to 207,819 kps (0.69c), while the ships are now at 21,439 kps (for an relative velocity of 186,380 kps [0.62c]) and so the missiles will cover that proposed first 250,000 km in just 1.34 seconds.
Okay, that's a longer time than I'd have thought. However the issue I think they'll have is weapon turning speed. Of course if you're headed on a direct intercept course with the target then you don't need to change heading at all - but you won't get the +250,000 km portion because you'd have splattered across their sidewall at -10km
(assuming they didn't roll enough to nick you with the edge of their wedge at -450 km). But assuming you're setting up for a near miss you'd have to change your heading continuously through your prolonged firing cycle to keep on target, and I don't think missiles or their warhead can pivot quickly enough to track like that (not while maintaining the crazy levels of precision pointing necessary to hit a target from those kind of ranges).
Let's look at about the closest reasonable pass, say a closest approach of 10,000 km.
[2]. When the slant range hits -250,000 km in this chase scenario the missile will be 10,000 km offset to the side of the target and 249,799.9 km behind (pointing at an an angle from flight path of 2.292°). So for the +/- 250,000 km slant range it'll actually cover a forward distance of "only" 499,599.8 km, and do so in 2.68 seconds. In that time it needs to whip around 175.416°, for an
average rotational rate of 65.440°/s. That's not too bad. But let's look an the near-peak rate. As it goes from +/- 100 km from passing through its closest point of 10,000 km away from target it has to swing through 1.146° in just 0.0010731 seconds; for an average rotation rate during that 200 km of forward travel of 1067.956°/s
Okay, that's only 178 RPM, but contently varying your rotation rate from nearly zero up to over 178 rpm and back down to nearly zero; all while maintaining a sub-radian precision in your point of aim is a huge, huge, ask!
And remember, these conditions were set up to give the missiles as
low an overtake velocity as plausible. Usually they'll have closing speeds about 20% faster, which would cause rotation rates in this scenario to be about 30% faster.
---
[1] As I understand it you were using -250,000 for before the missile made closest approach and +250,000 for after the missile had blown by the target and was shooting back at it -- so that's how I'm using them here1)
[2] For these scenarios I'm ignoring ship acceleration; as it would greatly complicate the calculations and at the velocities involved the effect of 3 more seconds of acceleration should be negligible.