Yeah I think you've got it.
Splitters for both the balance leads and the main leads. Your red boxes exposed in a panel.
The word "manifold" I used is not the best word. "Patch bay" or "patch panel" would have been better.
Basically a hole cut in a box with your connectors (red boxes) exposed.
If these are not panel mount connectors, you may need to use something like hot glue to fix them mechanically, or 3d print a housing.
Or you could get panel mount connectors and do a bit of soldering.
Once again, I'm not a LiPo expert, but cell-balancing will probably happen by default each time you charge the batteries, i.e. the charger will charge them all to 4.2V, or 4.1V, or 4.0 (or whatever you've set it to). Or when you discharge them on purpose to 3.8V for storage.
They will become slightly unbalanced during use, which is normal.
For example, say you charge the batteries overnight to 4.1V per cell (which takes a few hours). The next morning you disconnect the chargers. At this point the cell voltages are 4.1V, 4.1V, 4.1V, 4.1V, 4.1V, 4.1V, 4.1V, 4.1V, 4.1V, 4.1V, etc.
Then connect the bike harness and the LVA's and go for a 2 hour ride. You get back home and the average cell voltage is now 3.8V per cell. But practically there will be a distribution of voltages around 3.8V, so 3.81V, 3.77V, 3.76V, 3.82V, 3.84V, 3.79V, etc.. which means they are slightly unbalanced.
Then you put them all on the charger again, and after the charge they should all be 4.1V, 4.1V, 4.1V, 4.1V, 4.1V, 4.1V, 4.1V, 4.1V, 4.1V, 4.1V, etc. Which means they are balanced again.
If you don't charge them and you leave them unbalanced near 3.8V, you can just store them like that - being unbalanced is not bad per se, as long as any particular cell is not too flat or too charged when storing.
If they're still pretty highly charged (say above 4.0V), and you want to store the bike for a week or two, it's better practice to discharge the cells to around 3.8V.
Unbalanced cells are just inefficient at the end of the day. If one cell is sitting at 4.0V and another at 3.6V, then you'll only be able to ride until the lowest cell hits say 3.3V if you don't want to damage the cell. Which leaves the other cell at say 3.7V with capacity to do work, but it can't because the low cell would also get drained below the damage voltage.