Latest firmware for the 53xx is here and is dated last month. So grab that and install it first. (The latest firmware on Xerox.com is never the latest, it is always the current "General Release", there is almost always a newer firmware that is considered a "Spar" which is a General release modified to fix known issues in the General release.)
The Firmware you listed is for an entirely different family of machines, it runs the 7120 specifically.
The fault you are getting is because the printer does not understand the encryption used by the server.
It very much appears that Google is doing another staged security rollout, like they did last year that mandated the use of 2048 Encryption, and because it is a staged rollout, it goes server to server, so the machine will work today, but not tomorrow. Google does all their updates this way. Xerox is getting many reports from many customers on many machine families about that particular error. So install the latest spar, if it still fails, ping "smtp.gmail.com" a few times from different PC's and collect some different IP addresses, cycle through them on the printer and use whichever works (Because they stage their rollouts you will typically find one that has not had the update done yet) and use that while waiting for Xerox to get a firmware built to meet the standards.
So just update the firmware and change no settings and all should be well.