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It seems the Berkeley and UChicago want all information at the time you submit your application. My applications are all ready to submit. However, I am currently waiting for a letter of recommendation from a professor I had in undergrad. I know these two schools would rather I submit 2 academic letters of recommendation. Currently, I have 1 academic letter ready (the one I'm waiting on will make 2) and 1 letter from an attorney I work under (I graduated two years ago and have been working as a paralegal since). This professor said he'd have my letter ready early this month, but I also know he's bad with deadlines. I may be waiting until December to submit my application to the two schools if I hold out for this LOR.

Is it better to wait so that I have the two academic letters of recommendation Berkeley and UChicago prefer (but don't require) or submit now, while it's still a little early in the cycle?

Anything before December is "early" for admissions purposes. I don't think you'd be disadvantaged by waiting a few more weeks. But don't be shy about reminding/bugging your prof. If you haven't heard from him, I think a polite reminder email (or phone call if he's not an email person) early next week would be warranted.