I also worked as a consultant for many years and I can say this sounds
like a people/process problem, not a technical one. And as such I do
not expect that technical arguments will carry much weight (unless
they significantly effect the process). As such, if you have no
alternative process to "sell" then you will find this very difficult.
Some others have provided good process suggestions but unless you can
marry that to the people in your organization and help realize the
final business goals too, you will be stuck with the group decision.
Unfortunately it is the cost of working in a team. On the plus side,
this is usually best as "winning" implies ownership and you will be
left working every problem associated with the result until it's
operating smoothly.
Or to put it another way, "be careful what you wish for, you just
might get it". If you do decide to work through and "sell" a ledger
based process make sure not to criticize GnuCash unless it is over
something absolutely fundamental (i.e. we cannot achieve goal X with
that tool). Just focus on optimizing your process for the people so
that they see "ledger = less work".
As others have mentioned I believe that conflicts will be your
critical road-block in managing a multi-user process. 'git' is not a
solution and, a suggestion that it is will likely kill any
representation of yourself as a sane work colleague (unless of course
your colleagues are already 'git' proficient). This will lead to
consolidation efforts among multiple user files and this is the
opposite result you want (i.e. "ledger = more work") and thus you will
need to find a significant process improvement to offset that.
IMO the strongest argument is independence. The ability to allow
independent reporting to be consolidated quickly and effectively. To
gradually grow the costing structure to match the different parts of
an organization and discover and develop the higher level reporting
structure inline with that development. This requires long-term
investment in the process but as cost control is so fundamental to a
successful organization, this is more a positive assertion of
engagement than a problem. The same process is far less dynamic in a
centralized (database like) system, where we must globally define the
different cost centers and accounts for all departments at once.
Likewise they must be revised and consolidated at once. The reality
is that this very rarely happens and it can cause your cost analysis
to stagnate with an archaic or faulty view of your organization.
Good luck and have fun (it makes the battle easier).