I can not see, how the error "Error parsing response to JSON: Error: Unclosed root tag" indicates any relationship to a number of more than 1000 work items. I could see that at some point in the communication buffer size could be an issue. This might cause an issue when trying to serialize/deserialize json for or after transfer. It could be a defect as well. There is pretty much no information what you do, so no way of telling.  

Regardless of what method you use, despite some rumors it would be otherwise, resources on servers are limited and that is why solutions like paging or individually retrieving items exist. I am pretty sure, if you get each work item individually, you could export as many as you like using OSLC.

Note that JSON representation is not totally clear and might not be fully supported. See https://jazz.net/forum/questions/282584/how-to-return-data-in-json-format-in-eclipse-while-using-http-client-query-method . Mediatype application/rdf+xml should be fully supported.