Ah, I failed to grasp that. The DM is going to contemplate the declared moves (and any fair updates as the round is resolved) and adjudicate where along their intended paths each participant actually is at moments of interaction. Does that describe it correctly?*P1 has information - they know the basic distances of the goblins, the terrain, etc.
I would add that once P1 has declared that it's a noticeable part of the fiction. He's zeroed in on that 1 goblin, his allies and the goblins can both see it. That should turn the rest into fictional decisions rather than mechanical ones. In short, the declaration phase changes the fiction. Also, I think it's worth noting here that if another creature meets you in the middle - so to speak that you always have the option of attacking that creature instead.
For P2 their move is going to need a general direction. The idea isn't that they get to move wherever they want when their initiative comes up. The DM abjucates positioning based on your declaration. That detail is required. (For melee characters it's kind of built in if they are wanting to attack N1).
Honestly, I would like to know where you land with your players on this after a few sessions. I ran declare-first combat for years and when RPG design finally figured out how to create streamlined turn-sequences, we switched and never looked back. It strikes me that perhaps we gave up something we could well have demanded of our fiction (i.e. what you demand), in exchange for something that played so much more smoothly (for us) that we happily accommodated it into our fiction.I like how the dodge action functions under this system better. It feels more dynamic and response. You see multiple enemies about to gang up on you and so you attempt to defend. Other interesting actions N1 could have attempted would be to fall back and shoot with his bow. P1 might not be able to reach him then.
N2 moving and attacking P2 is going to create is going to create an interesting situation regarding if he gets there before he shoots.
I urge you to run through some sample turn orderings. I did so, and assumed that you couldn't have intended re-rolling initiative each round. The problem you will have to think about is that there are many - until the start (or end) of your next turn - effects in 5th edition that re-rolling each round is going to break.So far this feels good to me.
I'd just add that N2 is eligible to dash toward his intended target if he can't reach them to attack. If he did so, he likely closes the distance but doesn't find a good opportunity to attack after doing so.
*Initiative is going to be rerolled. So P1 cannot assume he will go first again. I probably could have made this more clear
Additionally, actions and reactions are spaced out with care by the game designers, and rolling each round is going to sometimes give sequences that are very powerful (or vulnerable). Such as cast, win initiative, cast. Combats will become more volatile in consequence, and sometimes that is going to feel bad at your table. For me, it is also in conflict with your professed desires: because you will have to gloss-over how some participant gains such tempo upbeats. From experience, that will sometimes feel SoD-breaking.