Mike,
The "settle in" is for event-based sync, to give the device time to actually connect (both WiFi and mobile data need some time to become usable after Android reports them as "connected"). If you're not using event based sync, you can just ignore it.
As for battery use, IMAP Push is very expensive, especially with Gmail (incomplete IMAP IDLE implementation, known since 2007, no plans to fix), especially if using more than 2-4 folders, especially when "messages per page" is set higher than the default 25 (this is how many recent messages the app looks at, every time it checks mail or gets a sync event in push mode).
So, the most obvious question is -- how many folders do you have in push mode? If more than 2-4, might want to reduce that. And do check "messages per page" in the account's "Options and folders", too.
More questions on this, or maybe my response didn't make sense? Don't hesitate to contact me directly at kmansoft / gmail.
Thanks.