Have you checked your voltage signals on the over the mast cables? This guy has them, correct? Normally when the chains start to stretch or need to be tightened, they wipe out the conductor wire and stretch them. Same thing happens on rech trucks with carriage mounted sol valves and Raymond OP's as well.

Did you check the integrity of the reverse switch? If the contactor closes in reverse it is most definetly the contactor, not usually the tip but the armature guides worn.( due to being mounted the way they are)

I don't replace the tips, I replace the contactor. These truck are notorious for contactor problems. Put it up on a block to get the drive tire off the floor, have someone drive the truck slowly in the direction that is failing, and reach in and jiggle the contactor tips. I think you will find your problem.

if all you did was replace the tips themselves you may want to go back and double check the insulators for wear. they do wear on one side after a while this can prohibit the movement of the armature and will not allow full travel of it. ultimately causing the tips to not make good contact or not contact at all.
if you can access the tips have someone get on the truck, (make sure the drive wheel is off the floor)
actuate the system without letting it move(in creep speed), wiggle the tips and see if the truck tries to move.
this will verify this problem.
if the contact area is enclosed and non-accessible then you just have to wing it i guess and take them apart.

I would say its the contact tips again if contactor is pulling in and you don't have travel in one direction only. Is it coding a 24 too? I have seen this with some of the crown SP's in the past. Some times you can clean the tips up abit and it will work fine for awhile, but if pitted bad you have to replace tips. Also check the guide pin on those GE contactors sometimes they break and don't allow tips to make good contact.