Good software is not designed by the central committee; The central committee screws up everything.
Good software evolves.
You need to forget all grandiose plans to fix the software, especially if the ideas come from academia. Become unprincipled with respect to practicality.
The software has already evolved a lot. If you attempt to recreate from scratch, you will almost certainly repeat previous errors, even if you avoid the current maintenance mess.
The problem is that the software has evolved towards external goodness, while ignoring maintainability goodness.
Make a secret plan to slowly evolve the software towards maintainability.
Slowly sneak maintainability and sound software practice in the back door when no one is looking.
Scream loudly about how big the mess is and how amazing it is that anyone can make any changes at all to it.
Make the point that it is not how well the elephant dances, but the fact that the elephant can be made to dance at all.
This will give you more time.