Thank you again Ken!
I got the below response from Chris at Support. I figured I would share with the Community in case someone else runs into the same issue in the future.
Blake
Hi Blake,
I've taken a look at the proper Autosynch, and I've compared it to an error in our Application Log that corresponds to the autosynch's most recent run date and time. The error I found in our Application Log is "QUERY_TIMEOUT: Your query request was running for too long." What this suggests is that your autosynch attempted to pull too much information, and timed out before it was able to finish processing everything being pulled into your database. What I'd recommend at this point is to run your autosynch for a specific timeframe, pulling in your contacts in batches, until you get to a current number of contacts (the criteria for when this would be would be up to you).
You can do this by following these steps:
1) Go to Settings > Setup > Integration
2) Navigate to your Autosynch area and click your Get Contacts autosynch
3) Go to Auto Synch Options in the top-right corner, and select "Run Autosynch (Ignore Date Filter)
4) Choose the "Specify Filter" option (Number 2), and pick the date range you'd like to run your autosynch within.
5) Repeat until you have the correct data in your sandbox instance. The autosynch should function normally after performing this action
The other option you have is to modify your External Call filter to be more specific, (i.e., cause it to exclude more SFDC contacts than it currently does). There are many methods for doing this, but the one I find most effective is to include a "Sandbox Contact" flag on a selection of contacts within Salesforce, and modify your autosynch to only pull those people. Either method is viable, however option 1 would be my preferred method for dealing with this issue.
Please attempt to implement this and let us know how it goes. If you have any questions about this process, please feel free to let us know through this SR.
Take Care,
Chris