[exim] smtp timeouts sending to google servers

I am experiencing problems when trying to deliver to Google's email servers.

My emails are timing out while trying to send.  The emails retry, but
I'm seeing delivers times of 10+ hours for some emails.

I suspect that Google are doing this on purpose to throttle the number
of emails I'm sending.

I had two users who once per week would send out a mailshot to between
them maybe 1000 recipients. A small percentage of these would fail.

questions

1) Is there any contact point within Google that I can use to try to get
me unblocked?
2) Is there anything I can do to improve my reputation with Google? I am
working through their bulk email sender guidelines?
3) Until I fix the underlying problems, is it possible to route all
emails destined to google servers through another of my Exim boxes?
4) Does anyone have any general advice to prevent this sort of thing
happening again, e.g. how we can continue to send out our mailshots?