I know what you mean however StoreYa's limit is 10,000 products per store.
My suggestion is to create a StoreYa specific store with 10,000 products or less. This way you can control exactly what products will be imported.
Additionally, your store has 295 categories most of which have very complicated saved searches, which take a long time to generate. This is causing a time-out on StoreYa's side.