Why do you say "...can work with any even number"?
I don't see any difference between even and odd numbers.
See method 4 of your LMGTFY. It's two pairs of two cross connected batteries for a total of four batteries. Similarly, you can connect two pairs of three batteries (using a star point connection on three batteries) to achieve the same balance.
But you always have only TWO corner connections and two feed wires, so to achieve balance you can only achieve balance with EVEN numbers.
I do like it, it's a simple and elegant solution, but it adds resistance to the circuit. Your total loop resistance for each battery is:
Positive feed wire + Internal battery resistance + Cross connect wire + Negative feed wire.
This works great when the batteries are close to each other, because your cross connects are kept short.
But the OPs method eliminates the cross connect wire resistance from the loop. PLUS: every time you add another battery, it effectively parallels more wires back to the inverter/charger, achieving even lower resistance of the feed wires.
So let's look at the math to see if the OPs method can balance. The resistance per foot for copper wire you get from a lookup table online.
Side note: Make sure you're actually using copper wire and not something else. I bought some cheap jumper cables thinking they were a good source for large gauge copper wire, but they were copper plated aluminum, so they didn't follow the tables for copper. Similarly, you'll find jumper cables that only look like big wire but it's actually a small wire with lots of insulation there to fool you.
Resistance per foot x feet of feed wire = total wire resistance.
Round trip resistance = 2 x wire resistance (using same gauge wire, and ignoring the battery's internal resistance)
For the longer run it's the same equation, but with more feet of wire:
To balance two legs, you chose a larger gauge wire that matches the resistance of shorter wire. Three, four, or more batteries, just continue to match the resistance:
6 AWG @ 2 feet = 1.58 mOhms round trip.
0 AWG @ 8 feet = 1.57 mOhms round trip.
This now makes sense, since the ratio of the 8 foot and 2 foot legs is 4:1, so the wire gauge has to be the inverse: 1:4 (#6 to #4 to #2 to #1 to #0 is also four steps of increasing diameter).
Normally, 6 AWG would be considered too small for a battery, but this is an example where a really short wire doesn't need to be as large as a big battery cable. "Ampacity" tables are available in two forms, one for longer runs, and one for interchassis wiring. A short wire doesn't have to follow the long run ampacity table because its resistance is kept small.
Now compare that with cross-connect method, if you need to span a 10 foot long cross connect between two batteries, the wire will add more resistance to the loop. To make this anywhere comparable to the OPs home-run method, you'd need really, really (really!) large cross connects. I'm not saying this can't be done, but it is a big trade-off. Actual cable routing pathways and big things in the way often determine what wiring method you CAN use, so his routing will be ultimately dictated by his vehicle layout.
A 0 AWG cross connect that is 10 feet long adds 0.98 mOhms to the loop.
That's really a really big number compared to 1.57 mOhms. So let's try even bigger wire:
00 gauge is 0.78 mOhms,
000 gauge is 0.62 mOhms, and
0000 gauge is 0.48 mOhms -- which is still a large number compared to 1.57 mOhms and huge 0000 gauge wire is nothing you want to deal with.
So it can't be practically done without a big penalty. But it achieves balance -- without doing ANY math. That's why it's recommended.
From what I see here, the cross connect method has a serious flaw when the batteries are far apart, but a real benefit when they're close to each other.
There's more to this if the OP provides any specific constraints of his rig, so I'm not ready to say quod erat demonstrandum.
