Ask HN: Inherited the worst code and tech team I have ever seen. How to fix it?

I have to find a strategy to fix this development team without managing them directly. Here is an overview:

- this code generates more than 20 million dollars a year of revenue

- it runs on PHP

- it has been developed for 12 years directly on production with no source control ( hello index-new_2021-test-john_v2.php )

- it doesn't use composer or any dependency management. It's all require_once.

- it doesn't use any framework

- the routing is managed exclusively as rewrites in NGInX ( the NGInX config is around 10,000 lines )

- no code has ever been deleted. Things are just added . I gather the reason for that is because it was developed on production directly and deleting things is too risky.

- the database structure is the same mess, no migrations, etc... When adding a column, because of the volume of data, they add a new table with a join.

- JS and CSS is the same. Multiple versions of jQuery fighting each other depending on which page you are or even on the same page.

- no MVC pattern of course, or whatever pattern. No templating library. It's PHP 2003 style.

- In many places I see controllers like files making curl requests to its own rest API (via domain name, not localhost) doing oauth authorizations, etc... Just to get the menu items or list of products...

- no caching ( but there is memcached but only used for sessions ...)

- team is 3 people, quite junior. One backend, one front, one iOS/android. Resistance to change is huge.

- productivity is abysmal which is understandable. The mess is just too huge to be able to build anything.

This business unit has a pretty aggressive roadmap as management and HQ has no real understanding of these blockers. And post COVID, budget is really tight.

I know a full rewrite is necessary, but how to balance it?