A quick update: After attempting to troubleshoot this with an escalation team, my entire OS started deteriorating. First, the OneDrive app continued to crash and be unusable. I followed all steps recommended - including deleting ALL office preference files and other related files, and nothing has worked to date.
Then, Outlook developed a Glitch (using 15.3, which is not part of Office 2011 but rather the stand-alone Office 365 download of the program) where it would not show current conference room times when I booked a meeting. THEN, all office apps began crashing within 5 seconds of opening.
Completely uninstalling and re-installing Office fixed the crashing issue with those apps. Crashing with OneDrive for Business and calendar issues with Outlook v15.3 remained.
At this point my company has attempted to completely re-image the machine to get everything back to a working state and I've been given an entirely new system. I won't be pursuing the OneDrive for Business for Mac beta again - I'll wait for the official stable software to come out (if it ever does).