REST API & Thumbnails

I have a client with 32 custom thumbnail sizes, we use REST API to create and update product information.
Is there a method to exclude custom thumbnail sizes or a subset of sizes as clearly we wont want 32 size variations of the product images. besides max execution times out, currently set to 600 (5 mins) and if a product 2 or 3 images the count gets into the thousands. We obviously don’t want to extend that already generous timeout.
I’ve searched but cant see a method to exclude thumbnails from REST.