I think you're going to be out of luck unless you can disconnect the other 3rd party device. Changing priority is only for when messages 'collide' with each other on the CAN bus and need arbitration; it won't effect how the engine ECU reads them or decides what to do with them.
Is this other 3rd party device doing anything else, or can you simply disconnect it?
A long shot, and I don't know anything about the config capabilities of the John Deere, is maybe you can configure the John Deere engine to only accept the TSC1 message from a specific source address so that it ignore the message from the other device. I wouldn't expect that to be a configurable option, but maybe it is.