Liz, If I could chime in... I noticed something similar when going to my bank's web page yesterday (just didn't have time to report it) which also hung on a TLS handshake to AWS. To add to this, it seems like it's happening very sporadically (or transitionally, as I explain later) and eventually clears. AWS switches their IPs around very often (a pure annoyance from a web security standpoint, imo). It's very possible that when they do that, the IP caching used in the DNS acceleration may get confused and try to handshake with the wrong IP, thus causing a TLS error. If that's the case, there might need to be exceptions made for AWS and any other cloud/server farms that tend to do the same thing, like DigitalOcean, etc. I'd venture to guess this is part of the problem people were having going to amazon.com recently, as well.
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