Not that I've seen much need for a calculation of a craft's past position in the current iteration... There's the 'already passed' half of any plotted orbital path but right now that could just as easily be the segment from +0.5 to +1 orbits 'forward' (ignoring any encounter/dis-encounter transitions) as extrapolating backwards.
The same treatment (tied to the moving volume of space[1] of the same
two (or three) most significant influences) might not be able to produce something similar (not always being able to create a true closed orbit) but extrapolating backwards
could be done for that, the same as extrapolating forwards, at least to a point where (if one ignored change of frames) an equal amount (by time and/or distance) of forward orbital and rearward orbital brings the tracks to the same celestial 'longitude' from the primary orbital body, even if they don't meet there. The transition point to now being in two(/three)
different influences (losing one moon and gaining another, or gaining the sun instead of one/vice-versa) could probably be similarly treated as the single-change-of-influence transitions as of now, i.e. do not draw the path beyond that encounter-point and instead draw the new 'continuation' on the moving frame that is destined to meet the current one.
(I can see what I'm explaining quite clearly in my mind's eye, but I'm not sure it's properly survived the transition to explanatory text. Apologies if I've made the result too convoluted, but I think you
should be able to work out what I mean, even if you don;'t agree with it..!)
But, yes, the maths is more complex to create the 'railroad' for coasting (and warping) on. Still simpler than adding a propulsive delta-V component to the predicted path.

Anyway, let it be the way it is, I'm just postulating. Perhaps out of my nether regions, for which I might need to apologise...
[1] A constantly rotating frame of reference, around the barycentre of the two bodies concerned (typically NAMND to the centre of the larger, rotating with the same periodicty as the smaller's orbital plan), upon which a more complex 'orbital ellipse' would be plotted that could be like an oscillating spiral if sent far enough in either direction. Plotted on whatever frame the normal orbits-cam uses (rotationally static to the stellar background, I think, but centred around the main orbital body) it might look strange[2], but as understandable by the experienced orbital navigator as existing "slingshot" orbit->moon encounter->moon-de-encounter->onwards tracks.
[2]
That's a perfectly closed path. A slightly different trajectory would create a path that (for any given "currently at" point in the orbit) will deviate both prograde and retrograde legs of the 'orbit' by increasing amounts. Maybe at some point breaking out into a different sphere of influence. But even if it's tight enough that it stays within those bounds[3], the diametrically 'opposite' point in the orbit[4] could be a disconnection between the two equi-opposite 'leg-ends'.
[3] In that picture it might depend on no major Martian/Venusian-orbit planet finding itself assigned as more of an influence than the Earth is, as it transition via the long, far left side of that frame's horse-shoe, under my limited-but-N>1 influence scheme. In fact, I'm not sure if this
particularly extreme example would work under my proposed scheme... But it'd be nice if it could!!!
[4] Imagining the tracked object is currently on the
far left stretch (effectively retrograde, by that frame's standards, but celestially still prograde), the 'opposite' point on the orbit would actually be on the lower, sunwards, stretch, on exactly the same side. Move the object position round one way and the equi-opposite point would (at a different speed) retreat in the other direction, of course.