Your diagnosis of the problem doesn't sound right. Why would your program crash just because of a slow component? What you should do is mock your calls to parseJson so that it always returns a static JsonNode containing test values. This would confirm that parsing JSON is the cause if the crashes stop.
It also sounds like you need more granular tests as well, to confirm that each component works as expected in isolation.
Thank you for your reply. I now understand that parseJson is unlikely to be the source of the crash.
I feel very sorry that I cannot present the source code.