For a few key activities, there are two different teams that feel their director should be accountable.
They don't get to "feel" about this. Accountability in a RACI sense is a function of organizational structure and appropriate delegation of authority from executive leadership. If the lines of accountability are unclear then executive leadership needs to get involved.
Accountability should either be defined by policy, clearly delegated by executive leadership, or formally authorized by a role or steering body that is empowered to delegate some or all of its own accountability for a given activity. If the roles that are accountable for specific items remain unclear, then the role ultimately accountable for the company's "major digital transformation project" needs to define and communicate the delegated accountabilities more effectively.
Organizationally, Accountability is Delegated or Assigned
It sounds like both teams (and you) are confusing accountability and responsibility. In a standard RACI matrix, the roles for responsibility and accountability are defined as:
- Those who do the work to complete the task. There is at least one role with a participation type of responsible, although others can be delegated to assist in the work required[.]
- The one ultimately answerable for the correct and thorough completion of the deliverable or task, the one who ensures the prerequisites of the task are met and who delegates the work to those responsible. In other words, an accountable must sign off (approve) work that responsible provides. There must be only one accountable specified for each task or deliverable.
There are certainly other models, but if you're doing RACI then you are drawing a distinction between responsibility (which pragmatically means "the task performers" in a RACI context) and accountability, which in most real-world contexts means the oversight role or budgetary authority for "responsible."
In the case of accountability, this should not be a case of alignment or consensus. In most companies of any significant size, this type of accountability is delegated through various means, but ultimately comes from the operating authority of executive management. For example, a CISO, CIO, or CITO with a compliance mandate might delegate some or all of the company's PCI DSS compliance to a specific officer, role, or team, who is then accountable to that officer for ensuring that the compliance requirements are met in a satisfactory way by whoever is doing the actual work (e.g. the responsible roles or teams). The accountable role is the one on the hook for ensuring the work is done, fit for purpose, and meets objectives, but is it not inherently the role that performs the tasks needed to deliver the objective.
If teams want to fight over "who gets the blame when stuff doesn't get done," you have a culture problem. The line of delegated authority should be clearly defined from the top down, meaning that it is the job of executive leadership or a suitably-empowered steering body to assign accountability.
In the case of a "major digital transformation project" that likely affects the entire company, someone at the executive level should already be sponsoring the initiative and is likely the source of accountability for the overall program. If you don't already know who that is, or don't have a direct line of communications with them, then you should start by talking to your immediate leadership and ask them to assist in untangling the lines of delegated accountability.
Treating this as a consensus-building exercise is a non-starter, simply because it is an organizational gap that must be resolved at the organizational leadership level. Collaboration and soft-power influence are great tools, especially in an agile context, but they are not usually the right solutions for structural problems that can only be solved through appropriate delegation of authority.