Thank you for your question. Philip Pfeifer is a wonderful certified EOS Implementer who has an excellent response to your question.
Here's what he suggests:
For starters, the leadership team should implement EOS and specifically create an accountability chart, start running a weekly Level 10 Meeting and create their Vision using the VTO using the Proven Process. This will solve the accountability and communication for the company.
Separately, the board should decide how often it wants to meet and should create an agenda that ensures all of the board members are on the same page. They should review the VTO and accountability chart that the leadership team did and either agree or work out changes. They should also issue solve any other items that require their attention. This will resolve the accountability and communication at the board level.
Given there are 2 members of the board on the leadership team, this should connect the circles and get and keep everyone aligned.