I took two different approaches to fix the issue. On the inside of the peninsula, I was able to put in a new piece of plywood and give myself the support I needed.
On the opposite site, the situation was a bit different as that side had been cut from a large piece of plywood with a smaller trim piece added. This meant that the solution on the opposite side wasn't a good fit.
Enter a biscuit joiner.
|5 biscuits and some glue.. Lots of clamps to keep it together while it dried.|