RE: "UPS Service is currently unavailable, try again later. The underlying connection was closed"
I just tested the UPS plugin in 4.60 and it works OK.
Call UPS support and ask them to switch your account to a live account (production).
In the UPS Plugin Settings, unselect "Use sandbox". Verify that you have entered correct
Account number
Access Key
Username
Password
If you continue to see an error in the log, then it could be that your TLS (Transport Layer Security) version is not at least 1.1. Where are you hosting your site - your own server, or hosted/cloud?
Locally, or if you can get to the DOS prompt on a VPS, you can use PowerShell to see what TLS you have:
[enum]::GetNames([System.Net.SecurityProtocolType])