Worth watching this series of public statements by senior IT managers (often .gov.uk) for the UK about why their orgs need to switch to agile approaches.
The clip embedded below is very dry, and the sound isn't very good. However, it's a lead in to a series of other clips - go through to Youtube and watch them all - or at least a bunch. Who knows, maybe it will help you in your transformation negotiation.
Maybe it's time to switch to Lean.