I think that Agile in principle is a good idea, keep iterations small and work on the issues together and deliver working products. The missing piece I think is that PDCA (Plan/Do/Check/Act) cycle isn't being done correctly. The idea is not just to improve the product but to improve the process of creating the product. This may mean you stray way of the path of the Agile system but that doesn't matter, the standard Agile process is just a starting point, it's your shop, create it how you like.

I like a saying from the LEAN manufacturing culture - "The Process is the Expert" but that comes with a caveat, each and every team member is a Process Engineer!