JSON Handler - Max JSON size exceeded

Does the API you're calling have additional parameters where you can limit/query only for certain fields? If so, I would try and minimizing the scope of your JSON response in the call itself only to the necessary fields and make sure that your query is only for a single object. Your only real avenue with how you're trying it is to minimize the response and get the size down. 

The only other idea I can imagine is to forego using the JSON resource fetch and use the generic webhook to get the info, in my experience the parsing of that response is reasonably the same but I've never had it return payload size issues.