In case you're not using default ruler set for authentication from library i would suggest you to test this. I can remember similar issue while using custom ruleset for authentication, not sure what the issue was at leased. Anyway default rule set worked fine and the issue was fixed immediately.
And a quick glance, it sounds like your proxy is behaving correctly for that mode but your browser isn't sending NTLM credentials. Does your browser authenticate correctly for other https sites?
By default, Chrome leverages the system settings for Internet Options, including what hosts, domains, and IPs to trust. Do your settings cover the address of the proxy?
If you'd be willing to post a rule trace export for affected gmail traffic and any kind of unaffected HTTPS requests, I can take a peak at it. You can PM me if you want to send it directly instead of posting it.
Ugh, I'm sorry , I never saw your question about posting logs. I don't think you can attach whole files or anything like that, but if you're able to run a rule trace and export the results, you could upload them online somewhere and link to them. Or you can send me a direct message to exchange contact info if you're able to share via email but not by public post.
I think you are not using the default rule set.
The default criteria of "Authenticate With User Database" (in your case "Authenticate with AD Database") should be:
"Authentication.IsAuthenticated equals false AND
Authentication.Failed equals false"
I am not sure if this will solve your issue, but I recommend to import the default rule set from library, make your adjustments (e.g. Skip Authorization for Client IP's) and test it again.
If it is still not working please create a new service request and provide a Feedback file, Rule Engine and Connection Tracing files for troubleshooting.