Not long. Replacing electronics is super quick*. Whole operation took about four months, I guess. It takes about two weeks for my warships to travel from Okinawa to Earth, about three weeks to refit, and then another two weeks to return to the front. I did half the fleet at a go, with the other half sitting on the gate loaded up with those short-range Harpoon missiles.
Building the new long-range missiles took a lot longer than refitting the ships.
Update: The Second Push was a qualified success, but our position is shaky.
We pushed into BV again, this time armed with sensors and missiles that can reach around 300m km. In previous pushes, we'd left one fleet guarding the gate and a second pushing toward the homeworld. This time we left the rear unsecured and pushed in with everything--1 AM cruiser, 2 command cruisers with 20 launchers each, 4 cruisers with 40 launchers each, and 4 antimissile frigates with 20 launchers each, plus three colliers. The cruisers are all 16,000 tons. The frigates and colliers are 8,000.
We carried about 900 of the new long-range Lance Mk1s, or four and a half full volleys.
We picked off about ten isolated ships moving alone or in small groups. We saw a lot more slow ships this time. Maybe the enemy is throwing everything including the kitchen sink at us this time? Or maybe those slow ships were in the field last time too and we just never noticed them because they were too slow to catch us and we were too blind to see them.
We found an extremely large task group of Betas, somewhere on the order of fifty ships of displacements from 10,000 to 30,000. This fleet doesn't appear to have much reach, and moves at around 2500km/s, so it's no threat to our fleet. But it's huge, and we expended our entire store of ammo and destroyed only 80,000 tons of what must have been a 750,000-ton fleet., then escaped without incident.
This fleet presents a problem.
If it remains in BV? Then we can just go home, reload, come back, kill a few more, and grind it down. But we don't have many Lances on hand, and the production pipeline is slow. To kill it quickly, we'd have to use our very large store of old Sparrows (100m km) and Harpoons (45m km). We don't know how many of those ships are armed with missiles, and we don't know the range of the missiles they may be carrying. But if any significant number of them have got missiles, our fleet would almost certainly be destroyed if we were to get near enough to them to use our short-range missiles.
If that fleet pushes into Okinawa, we're in trouble.
We've got excellent antimissiles, and large supplies of these on Mare Infinitus (our colony in Okinawa system.) But a fleet that size, if they're mostly missile boats, will be able to easily overwhelm our missile defenses, even if we're sitting at the colony and can reload from the surface.
If they push in, we'll have three options:
1. Defend Okinawa. We can maybe hold it, IF the enemy is composed largely of beam- and gun-equipped boats, or if they've got way less ammo than you'd reasonably expect.
2. Abandon Okinawa and fall back. Earth is four jumps away. It'd probably take them a while to find it, and we've got listening posts all along the route. We'd see them coming well in advance.
3. "The Enemy's Gate Is Down." Abandon Okinawa, go around their huge but slow fleet, and do whatever damage we can to their homeworld.
Whatever happens, our very next move is to withdraw the 2nd Infantry and 4th Armored divisions from Okinawa. There'll be no time to move them if the enemy attacks, and they'd take an extremely long time to replace. They were moved to Okinawa in anticipation of a much easier war than this one turned out to be. Now that it's clearly going to be a long hard slog, there's no point keeping the ground-pounders in harm's way. There'll be plenty of time to bring them up from Earth when we've achieved air superiority in the BV system.
*As a general rule, I've found that replacing sensors & fire controls is cheap and fast. Replacing armor or magazines isn't bad. Replacing launchers is painful. Replacing engines is so costly and slow that it's hardly ever worth doing.