First thing to address those frustrations was to set expectations with the product management team. In their approach, they really wanted to have a lot of drop-in interaction with the engineers, which worked...well, about as well as one would expect it to work.

So, what it took me doing was learning more about the product management daily process. It turned out that what drove a lot of the communication needs of the product management team was a desire for status updates because (drum-roll please) they couldn't articulate it sufficiently to the executive team.

We drove toward what information was needed and how timely, then figured out how we in engineering could supply product mgmt with that info while staying in the wheelhouse of our own flow. So, evaluation of things like JIRA (Atlassian), Redmine and other tools to coordinate product management actions with engineering actions. It took a little while, but it required everyone all around to work together in expected ways to lower those frustration barriers.

Since the only frustration seems to be a lack of immediate and instant access to the engineers, I'd imagine that the fix here would be for the product management team to adjust their expectations and communicate better.

Many managers consider frequent communication as being good communication, but more often than not its actually very bad. It is a signal that people are not thinking through what they are trying to communicate. Some trivial barriers, such as a door or forcing people to walk over, are often a good thing, because they force people to evaluate what they are communicating and whether it is worth the effort.