Wow, looking at your third (picture 7) and fourth (picture

to last pictures, your idlers definitely don't look in line.
Picture 8 looks like the idler screw isn't tightened up?!
As for the play of the sprocket on the D, that would most likely cause the screw to undo, under driving load, and with the weight of the metal tracks, the sprocket would be forced to work back and forth on the shaft, the screw that holds the sprocket on the shaft is too small a size to lock tight enough to stop it happening without risking snapping the screw.
The thread lock and a toothed lock washer would help to keep the screw in place. Also something in the sprocket D, like a little, and I do mean little amount of blue tack may eliminated the wobble. Also, it would benefit to fit drive shaft support bearings that attach to the hull.
For the idlers, I would recommend a Henntech idler adjuster.
Tamiya lovers are going to cherish what I'm about to say now, sadly, Heng Long tanks are a bit hit and miss, especially with their quality control and assembly line. But, that being said, for the price, they do make a good entry into RC tanking, especially if like me, you don't mind the challenge of getting them to run.
Now the choice is yours, do you spend roughly 200 quid on a complete Taigen rolling chassis and discard the chassis you have. Or do you just do the necessary modifications to what you have? The two I suggested above would be around 50 quid.
You would also benefit from what we call clocking, which is done to the first and last road wheel suspension springs. An extra little hole is drilled in the chassis where the suspension springs are retained, about 2.5mm clockwise in the round slot. This will reduce those end wheels from pushing up too easily when the tank is running, as the tracks have a tendency to pull those wheels up and make the track tension loose. It all adds up to cause track problems.
Edit, just realised you are in the states, no wonder you're up so late and past my bed time lol. Therefore I'm not sure how much those items I mentioned would cost you over there.