stuff >> staff ?
Listening in on the conversation between your existing (third party) client and the (third party) Web Service would be a bad idea, if you can, you should stop using it altogether !
My thought is, you have put your data in the hands of a commercial operation, you now must work with them. Ask them to provide an additional service whereby you can ask for the data for Jon Doe, get it as you say, as json and then, now you have it, do with it what you want.
But without the cooperation of the third party, you are in trouble.
Do you have a plan about what happens to your data if the company holding goes out of business ?
Davo