Nope. If one panel is completely shaded and all other are in clear sunlight, a string inverter will output nominally the same power as an optimizer or microinverter system.
And each MPP channel should preferably have 10-13 panels to keep within the MPP range of the inverter, both on bright days (13 panels to avoid overvoltage) and on overcast days or at times noticeably different than solar noon (~10 panels). So in the OP's situation, it is probably best (if using a string inverter) to have 11, 12, 12, and 13 panels on 4 strings. Even better would be to add 2 panels in the open spots, if that is cheaper than going with a non-Tesla installer and an optimizer/microinverter setup.
Optimizers can help. To take a simple example for the OP's setup, if the chimney is casting a shadow anywhere on the bottom half of a single panel, then a string optimizer will probably get zero power from that panel (and full power from the others). But these are half cell panels, which means the upper half is capable of generating half the current that a fully illuminated panel can. An optimizer setup can use that upper half's output, or up to 170 watts more total output than a string setup. It is difficult to justify this increased power financially, however.
As already suggested, putting 12 unshaded panels on the east side will give just as much power as 12 unshaded panels on the west side. The maximum output will occur in the morning instead of afternoon, if that is an issue.