Hmmm, the solution seems obvious to me - the keyboard assembly needs to be disassembled and professionally cleaned. This is not really a difficult task, technically, but it can be time consuming and a bit tedious.
The problem is not likely to get better over time as the sticky syrup will start to collect dust, dirt and buttery pancake crumbs.
So from here, it seems you need to take it to a shop for professional cleaning, or live with an external mouse and hope all the keys continue to work properly.