Since our customer was looking for a more agile development & deployment workflow I personally recommend them switching from us to WPengine based only on Jason reputation and your technical expertise.
Almost a month has passed since they signed in for the service, $500 in fees and ~ $700 on WPmovers afterwards, they keep hosting with us and couldn't arrange a 0 downtime migration at all, neither provide a fixed quote for the migration.
Our case right know is being handle by Sergio, maybe you can talk with him and our customer to find a happy ending?
I've always been an advocate of WPengine and big fan, but after our bad experience and seeing others having similar issues too, I'm probably not recommending WPengine in a while..
Regards
M