I’m not sure the fore-aft tilt adjuster is needed for the planer in the box, because the framework of the jig is the reference surface upon which the planer car travels down the workpiece. The rotating drum takes away a left-right oriented LINE of wood, so the line must have left-right tilt correction, but fore-aft tilt is ineffective. If you get the framework & car traveling straight and true down the track, then the planer will do so too.
It’s probably most helpful for us to envision a normal stationary planer: The depth of cut is controlled by moving the cutter head up/down relative to the workpiece. Next we have remember that even though the power planer adjusts the front sole via its adjuster knob, that front sole doesn’t move relative to the workpiece, it’s always in direct contact with the workpiece, and the net result is that the cutter (and bulk of the power planer) is what moves up/down relative to the in-feed surface and workpiece, just like the stationary planer.
Therefore, in the car, we should fix the in-feed sole height and left-right tilt to be coplanar to the jig’s sliding car. That means the rear sole/cutter is what needs up-down adjusting relative to the car. This implies the rear sole must project below the floor of the car for clearance reasons.
It seems likely that the power planer’s intrinsic adjustments should be adequate to keep both of its soles coplanar, so I would probably start by double-stick taping an oversized Masonite hardboard or lexan shoe to the planer’s front sole, then mount that assembly into the body of the car, nicely coplanar, and then use the planar’s knob for fine depth of cut control. Course depth control will be nicely controlled by a series of parallel dados cut down the length of each of the rails at a gapping that’s slightly less than the overall maximum range of the control knob.