Hi TheEagle,
From your description, I understand that your web parts cannot work after service upgrade. To narrow down the issue, I recommend you share the following information with us for troubleshooting:
1) You mentioned that the webparts use $.getJson. Did you add self JQery code into webpart?
2) I notice that your public website is still SharePoint 2010 after service upgrade. I would like to explain that after service upgrade, you will have two public websites of the pre-upgrade one and new public website. Here is one article about how to upgrade your public website:
http://office.microsoft.com/en-us/office365-sharepoint-online-enterprise-help/upgrade-your-public-website-HA102801184.aspx?CTT=1
3) In the kb article above, I find one step is to re-insert CSS and scripts step. See the picture below:
So can you please copy the self-customized code to new public website for testing? The test result can help us to judge whether the issue is related to public website service upgrade.
Thanks,
Andy Sek