Best way to handle multi-select / array data with "completed custom data" and tokens?

The best way to support camelCase is to allow elements keys to use camelCase via /admin/structure/webform/config/elements and change the 'Element key pattern' to support Uppercase characters.

Does this solve your organizations use case?

Yes it does, thank you for your reply.
I somehow assumed that all keys had to be lowercase and totally missed the examples provided with each pattern.

CamelCase aside, is there an out-of-the-box way that Webform can post data with a custom structure (nested objects) while also still including arrays? Or, would this need to be done with some kind of custom handler?

Custom data only supports tokens. You would need to write custom code.