The problem is those roles are harder to find and grow into in smaller and even medium companies. Eng pay tops out unless you gain management responsibilities whereas at those large companies they will pay staff engineers somewhat proportionately to managers.
If your agency is the kind I think it is, the unit economics simply don't allow them to pay you above a certain rate for non management. There also won't be any significant career support.
Research the staff engineer track and if it's something you want to pursue I would consider a move to a larger company into a staff engineer track role, where there are plenty of people who want to be a manager and you can let them right all those battles while you keep your head down and build. You may not be at staff engineer level right now but you will have a career path.
My guess is you are also not being fairly compensated for your talents if you have developed this product line and are essentially the product owner as well. Even more reason to see if you can earn a lot more at a bigger company.