Three different ad platforms each write the same conversion to themselves using their own attribution model. When you aggregate the reports you end up well above the true conversion count. This isn't an error; it's a sales argument each platform has constructed in its own favour.
The warehouse-native solution
A server-side event stream is written to the warehouse; anonymous and identified profiles are merged through identity stitching. The attribution model is defined in the data layer in a versioned form. That gives you a single source and a transparent model.
A single source of truth
The vendor report stays as a reference point; decisions are based on the single truth in the warehouse. Which channel truly wins can only be stated with confidence after this setup is in place.