No one else who played the fixed version on Cafe of Broken Dreams last night has posted, so I'll just say what everybody in the server seemed to agree on: the whole push-pull game type just really isn't that fun.
Before you go any further with the map, I'd suggest really thinking about some of the problems with this game type and whether they're solvable or not, or even worth solving. Just some of my personal gripes:
1. Payload maps are always "narrow" in the sense that action is concentrated on a set path with one team always clustered around the cart. However, in a regular payload map, only Blu really needs to stick to that path, while Red can set up defenses or flank. In a payload race, the two teams have to balance between blocking the other's cart or pushing their own, but the two paths are usually far enough apart to provide some buffer space. In this push-pull arrangement, both teams need to be in the same little spot the whole time.
2. TF2's general sense of momentum is absent from this game type. In a 5 CP map - which this resembles - the time it takes for a point to cap or un-cap changes to encourage the attacking team to push forward. The slowest, most difficult part is the midpoint, and it goes faster from there.
In a payload map, the cart stops if no one is pushing it, then gradually begins to go back, so that Blu isn't punished for just getting pushed off the cart for a second or two and are able to maintain their push if they regroup fast enough.
As a hybrid of these game types, this push-pull seems to work on paper, as a 5 CP game is sort of like Blu and Red pushing one cart up from a valley where the incline gets shallower further from midpoint, so you can push it faster as you approach enemy base. However, what ends up happening is that Blu can push the cart halfway across the map, get their push knocked back by a single Medic-Pyro combo, and lose all their progress because Red can immediately begin pushing it the other direction. There is no equivalent to a normal cart's standstill time or the slow un-capping of points. Attackers' momentum is instantly broken.
3. Both of the previous two things give little incentive to ever put up a strong defense. At a final point in any game type, strong defense is necessary because the primary goal is to break the attackers' momentum long enough to either run down the clock or gather your own offensive push. Offensive momentum here can be broken by simply blowing them off the cart and pushing it the other way immediately.
4. The possibility of a stalemate is huge. In 5 CP, all the primary action can be locked down around a single area, but back-capping keeps stalemates to a minimum (in well designed maps, anyway). Back-capping instantly changes where the focus of combat needs to be. With this push-pull cart, there is no possibility of a back-cap, so the combat is always focused on the cart. If the cart is between second and final point when a standstill occurs and neither team can make a decisive push, there is nothing you can do.