October: After much discussion with Meraki and finally getting some answers from Microsoft we did make the decision that the issue was one of two problems:

1. Internet bandwidth was exceeding our 100MBps connection during busy times so the traffic was not able to return properly and would continue to disconnect once the bandwidth limit was reached

2. Microsoft stated that they use uPNP as the protocol to transfer traffic for XBox Live on the XBox 360. Meraki stated that since this is an older protocol and very outdated as well as not secure they do not support it on their enterprise firewall.

https://kb.meraki.com/knowledge_base/universal-plug-and-play-upnp-support

Meraki decided they would like to see what happened when we increased the bandwidth since IT was already in talks with several companies about a bandwidth increase this was used as their response for us to fulfill before we could move forward with the issue.