Congratulations, as far as I know you're the first to complete the Galilean Tour in realistic mode!
It must have taken a lot of planning.
No planning at all. I just took maximum payload which i possibly could bring to Jupiter at Realistic, and from that point i planed to look what i can invent. My first strategies were very naive and i laughed a lot when i saw how and why they catastrophically failed.
The 3rd strategy i invented was almost the same as you used there yourself:
link to forum thread.
But at Realistic level this strategy also fails. The real speeds are enormous and changing those speeds with your own fuel burning will eat away just awfully too much fuel. Simply increasing or decreasing your periapsis by yourself eats a lof of fuel already. And when i do this from super high apoapsis over Jupiter and then meet the moon there below - the difference in real speeds with any moon and my "passing by" is astronomical, i need to gain so much ΔV using my own fuel, that this is totally out of the question.
But your brilliant Closest Approach mod offered so much data for experiments, that i could try almost anything, and i tried very many different ways to navigate, to calculate the expected value of different trajectories, and it allowed me to find more fuel-saving manuevers. And i found a way, that eats almost no fuel at all for navigation between moons, especially for establishing first good orbit after entering Jupiter first time. Now i can bring any ship to any moon with very little of fuel burned, from any starting point, in any direction, skipping more than one orbit at once included.
That is why now it can be done with below than 60 tons of entire payload to Jupiter. And almost all that fuel will be spent for slowing down to take orbit, landing and taking off. It still eats fuel to slow down to get orbit around the moon, i can't imagine how we can find improvement here. Thus remaking landing module to be the smallest one possible we scale down the entire payload, since most part of this payload is fuel for landing and taking off and only smaller part is for slowing down before moons. And the part which is used for navigation between moons is tiny at all.
The best way i found so far is this.
First we use aerobreaking to lower apoapsis and burning fuel prograde both before and right after aerobreaking, because aerobreaking is not enough and we need to slowdown more or we will be thrown away somewhere far above Saturn. That is the only one unavoidable long burn. Because we are falling to Jupiter with 59 kilometers per second, what else can we do?
Then, when we got our first high apoapsis above Jupiter we cut engines off. On the next circle we slow down a little more with new aerobreaking, then little more again, and then we are picking any moon with which we want to start. Some moons are better of course, you know which and why, but the difference is not big. And we set out apoapsis to that moons orbit or little higher, in order to catch it soon.
While we keep our periapsis low, just near Jupiters atmosphere, since it is too expensive to move it on your own.
Then when we first catch any moon with correct vector of approach (similar to your Venus approach when you start VEEGA) - it will drag our periapsis for free and a lot higher, all we need to do is control our apoapsis with little Oberth burnings, so it would not go too far. With good initial vector of approach it doesn't require much burning. Plus when we do this correctional burning we again seek to meet with any other moon, with this one again for example - and Closest Approach exactly shows all possibilities at once for all 4 moons, here and now with no more work!
So, several more meets with correct vectors or ten-twenty more meets with worse vectors propels our periapsis to much higher level and once it is on the level of the moon we want to visit - we simply meet the moon there from its face, to give her away some of our extra speed, so we would not go to high apoapsis again. We can burn to gain orbit of this moon directly or can wait to overlap it later - it also makes little difference.
Then, when we want to go to the next moon - we do NOT burn our fuel again. We only escape the SOI of the moon we are currently orbiting. Once we escaped Soi we will meet this moon again over several laps, and when it will happen - we will go in with a vector, that gives us hard 90° turn to a side. I still don't sure which side is better, both are working fine. But one must be better of course.
It requires more testing. We can overlap once again to make hard 90° turn again to increase the effect, more and more times, if needed.
Then, when our orbits are destabilized enough - we can make new slingshots for free, since now our vector of approach is not parallel anymore. And collecting one or several slingshots propels you to your next moon's orbit almost for free.
I still didn't tried it with Earth yet, though it was my original idea. To improve VEEGA path and to reach Venus for the price of reaching Moon. Moon slinghots us away from Earth, then we destabilize several times on next meetings with Earth, and then we go to Venus to start VEEGA, and we only used fuel to reach Moon and no more!
It is also possible, that with little burn after well accumulated destabilizations we can go for EEEGA or EEEEGA directly, without Venus at all. But it requires more testing.
Moons of Saturn are much lighter in weight, thus my strategy may not work well there, so i plan to take maximum payload again, so i could have enough of extra fuel for experiments in Saturn system, to get to landing on all 8 moons with what i have.