It seems you're missing a small but important thing about balancers. They can be input balanced, and they can be output balanced. An output balanced balancer tries to fully satisfy its output, no matter unevenly pulling from the input. An input balanced balancer pulls equally from all input, and if this means the output cannot be fully satisfied, so be it.
What you want is balanced pulling from two wagons (or in your case: the buffers from your mod). This means, you want an input balanced balancer behind the inserters that pull from the wagons.
Your second balancer (the one on the right) is output balanced, but not input lane balanced. It doesn't pull equally from both input lanes. If the right lane of its output is blocked somewhere downstream, it will pull only from the left lane at its input. In this case, only the left lane of your first balancer tier is consumed. Since they are not symmetric (they are mirrored), this can result in uneven pull.
The balancers DaleStan posted are input balanced. The one on the right is the smallest 1-to-1 lane balancer known and the result of years of community research about belt and lane balancing - probably the first and most discussed topic about Factorio of all time, because that's the first non trivial topic that pops up for every player.
I guess you somehow gave up on balancing, because you use a mod to buffer the wagon output instead of pulling from the wagon into buffer chests. If you output to chests, the balancing gets even more difficult, because you not even have to balance between wagons, you also have to balance between the chests within a wagon scope. By using a mod, your're trying to cheat yourself out of that challenge.
If you want to profit from community research about balancers and not deal with the specifics, you can use the widely known balancer blueprints (kind of spoiler for players who want to figure it out theirselves, but huge time saver if you don't want to engineer again what has been engineered before):
An approach for a direct solution for your setup can be this:
You have 2 wagons to unload, so unload one wagon to one belt lane only and the other wagon to the other belt lane only. Then use the 1-to-1 lane balancer from DaleStan to balance. It will pull equally from both wagons, because each wagon fills only one lane and the balancer is a lane balancer and it's input balanced.