Can you re-architect the product from scratch? This should be doable if the raw building blocks (modules etc.) are properly designed and easily incorporated into a new design. If this is not the case, then all the more reason to rewrite the code!
As a CTO, there is a good chance the poster would not be materially involved in such an effort.
From a business perspective; something that works is more important than something that is well architected.
It can give OP a better feel for how the code is designed, and give them more opportunity to change things in a more structured way in the long term by repeating the process (rather than just fighting fires every time).
Ten year old battle tested spaghetti is more valuable than any benefits a complete re-write would provide.