But wouldn’t the western panels essentially be “in shade” in the morning, and the eastern facing panels be “in shade” in the evening? Even though the shade is created by the other side of the roof…the panels don’t know where the shade is coming from…just that they’re not getting sun. So if they’re tied together, it seems like one side will always bring the other down unless the sun is high in the sky and shining on both sides at the same time (for just a short part of the day).
No it doesn't quite work like that. Here is a somewhat crude explanation. For a single solar cell or panel, the current vs voltage curve looks like the below:
The inverter MPPT will try to adjust the voltage across the panel to maximize the power produced (Vmpp) which is represented by the area under the curve in grey. As the amount of sunlight hitting the panel changes, to first order only the height of the curve changes (i.e. the max current).
From now on for illustration simplicity I am going to ignore the knee and tail in the curve and just treat it as a perfect rectangle. If you have a string with 7 panels in series with uniform illumination the voltage of each panel is summed to give you a curve like below where I have squished the x-axis relative to the above graph.
The dotted lines just represent the Vmpp of the individual panels and the Vmpp of the string is 7 x Vmpp of a single panel. Now if one of the panels is shaded you have a curve that looks like this:
For panels wired in series the current through each panel has to be the same. If you keep the same operating voltage as without shading then the current of every panel is going to be limited by the shaded panel and the total area under the curve (power produced) would be lower than if the MPPT drops the voltage to the new Vmpp of the string. There is a bypass diode that allows the current flow through the shaded panel with no effect on the voltage effectively eliminating that panel from the string. I am ignoring for simplicity that each panel has multiple bypass diodes and essentially acts like several smaller panels in series.
Now if you have two strings wired in parallel the current of the parallel strings sums and the curve looks something like this if both strings are equally illuminated:
The power produced by each string is identical as if they were completely independent. Now if you have complete shading on one of the panels in String 2 it now looks like this:
The voltage drops on both strings so you not only lose power from the shading on String 2 but an equal amount of power from String 1.
If you now have have two strings that have different amounts of illumination the curve looks like this:
Again no issues if there is no shading within an individual string. You can imagine based on the above graphs what will happen if you do get some shading in this case. If there is shading on String 2, one of two things can happen depending on the relative illumination of the two strings. Like above the voltage could drop and you not only lose power due to the shading on String 2, but you also lose even more power from a higher producing panel in String 1. At a certain point the amount of power String 2 is producing gets so low that the Vmpp of the two strings is just equal to the Vmpp of String 1 (i.e. a single panel on String 1 is producing equal or greater power than all of String 2). In that case String 2 will produce almost no power but you get full production from String 1. This would be typically late in the day or early in the morning when String 2 is not producing much anyway.
All that said, it is probably not a huge loss in production unless you have significant shading during peak production times. Certainly it is worth asking Tesla if they would change your design, but I'm guessing that might be a difficult road given Tesla's responsiveness.
