They are in fact in a possible position, and the relative shadow geometry and all that is in fact correct for Sep 25 2387 around 19:30 UT. However, what ****s it up is the position of the Sun; it should be a smidgen or so farther south than it is, due to Jupiter's orbital inclination. Remember what I said about nitpickiest of nits? (I've attached proof from Celestia)
How the hell did it get that close to correct
what is this I don't even
I see what you mean by Sun being a few degrees too high. But I can't believe the random position I put the planet and moons in is actually that close to right date...