If I was in your position - I would push for integration of some sort while keeping the two products separate for now. Then have a separate team from both organizations start on a new product that borrows from both products. Obviously it’s easier said than done - ego have to be put to the side.
The advantage is you keep the status quo with minimal customer and cash flow distraction while working on integrated solution.
The advantage is you keep the status quo with minimal customer and cash flow distraction while working on integrated solution.