I think the essential point here is the desire for moving battles. Like @Lomsor, I don’t see them happening as a natural course of gameplay. They’ll happen because the gameplay systems are specifically designed for it. If there are stationary points of interest and no means of intercepting between those points of interest, the battles will be stationary.
The original warp system called for ships on different warp frequencies that progressively interfere with each other as they get closer to each other. So if there is a critical ship on its way to one of those stationary destinations, the opposing team should be able to fly out towards it, intercept it and try to destroy it or drive it off.
The difficulty there is the idea that the smallest ship might intercept and stop the largest ship. So it might be that some basic mass of ships is needed to drop a ship out of warp and force an engagement, while lesser masses might only slow the pace of movement a bit - allowing slower, larger ships to complete the intercept.
As @hrobertson points out, fights in the middle of a vacuum don’t have much to offer in the way of variety. As in: none. If INS got serious about such fights, they’d have to introduce some sort of meta-terrain. Magnetic fields, gravity variations, rarefied particle streams and so on. Stuff that would be trivial in any other context, but which could play a big role in how the various futuristic systems on these ships work. Alternately, allow the ships themselves to create this meta-terrain, as I’ve described in the past.
Unfortunately, all these things require additional work. Meta-terrain would involve all sorts of visualization work that wouldn’t be trivial to undertake.
Ultimately, I don’t see moving battles except as warp interception allows it over long distances. And this could be applied to big missiles. If they are warp objects, then other ships could fly out to slow or intercept them. So if a large enough mass of ships arrives, they can intercept the missile and take it out. The missiles could be of almost any size, and the mass of warp needed to knock them out of warp could also be tuned as needed.
I don’t see missiles (or even ships) that periodically drop out of warp for “reasons” being a workable solution. The timing of dropouts should be of the attacker’s choosing. If they are periodic and regular, then the attackers have to wait for one dropout, then start a clock, then wait for the next dropout and hope to be close enough to hit the target. It’s not a particularly good interception mechanic. I suppose missiles or ships could “advertise” the timing of their dropouts in some way, but waiting for that arbitrary timer to expire seems a bit cumbersome.