Tony,
I would guess that the wheels and/ or the the outer rails need to be cleaned, or the engines have traction tires on the wheels that hit the regular outer rail on the insulated rail section. If there are traction tires, does the engine do the same if it is running the opposite direction? (Not as in just throwing it in reverse, but picking the engine up and turning it around and running it)
On the rest of the track, the engine can get its return (or power) from both outer wheels which are typically fed from two conductors (the outer rails). On the insulated rail section, you lose one of those conductors, at least until a car bridges the insulated joint.
Of course, you have 4 solenoids running at one time (assuming the crossing gates are postwar types like the two other items), which is a fair amount of power. I would guess about 5 amps, or 60 to 75 watts. Your LW is rated at 125 watts peak I think, leaving around half the capacity for running the train. If it's also a postwar item, your LW may be pretty well maxed out. It may be time to add another LW for accessories (or whatever other transformer may be available) Disconnecting the accessories will likely determine if this is the case.
Hope this helps,
J White