Yah, as a rule, belts that are somewhat short should be adjusted with between 1 to 3mm of "play." It is measured by pressing down with a finger directly between the pulleys (not much pressure should be applied for this), and the amount the belt "bends" is the measurement. On long belts, go to the very center between pulleys, and measure in the same way. There should be between 3 to 5mm play. I usually just go to the outside measurement for short belts (3mm) and add 1mm to the outside for long belts (6mm). The standard for these measurements is: "tight" belts are good for more torque, and looser belts are good for more RPM. In my experience, looser belts also last longer.
Now mind....too loose will allow damage, if it is too loose (stripped teeth is the most common), and too tight will stretch a belt over time (much shorter a time than looser belts), and will fail faster.
If your belts are tighter than these measurement parameters, it is too tight.
This is why I recommend a carbon chassis kit for the TA06! I got mine a couple of years ago, when the TA06 was a new release, and thought the same, about the battery door. Almost any carbon chassis kit is a major improvement. The Exotek conversion has a "swing away" electronics plate, so the battery can be slid in or out from the side. The RSector conversion is top-load. Since I'm not a fan of "swing away" anything, I opted for the RSector, and am very happy with it. It is the least expensive, and comes with a new aluminum steering assembly that puts the servo on the right side, to better balance the chassis.
Yah....I forget the TA06 is gear driven in the rear end - No concentric. That makes things a little more complicated, as a new belt will have to be purchased. I forget which - either CS Junkies or DriftMission has a link where you can get Tetsujin belts in whatever length you need. Rather than scour the web looking for a belt supplier, just go to either of those sites and look for the Tetsujin link. Count the teeth on the long belt. You will need a belt approx. the number of extra teeth that is added at the front/center pulley. I'm not certain you will need a front belt, though. I think just using the spacer method and concentrics, you can mount the size pulleys you need, and everything will go together O.K.