Overall, I am fairly happy with Support actually. Perhaps it works well for us being in a dramatically different timezone but I usually get a reasonable response overnight. When logging issues, it helps massively if you can submit some screenshots, or better yet, a video with some audio explaining what is going on. Having said that, my top wish-list for Support/Account relationship is:
Create a new incident status in Zendesk for Unresolved defects (e.g. bugs which Dev have chosen not to prioritise a fix for)
Likewise, create a new status to use for feature/design/logic defects which are currently fended off by Support for us to log to the Idea Exchange.
Have your US-based Account Managers incentivised towards customer engagement, rather than purely sales. I only hear from ours at annual renewal time. Our local reps in Australia (WMA) are great but I don't feel like I have a connection with the head office organisation other than some great Product Managers who reach out at times.
David Cornwell Pentana Solutions