> or perhaps adjusting the order of the json output affects it to produce lower-quality results.

The order of the output fields can actually be used to tune performance of the outputs. It can be helpful to force the LLM to reason about specific fields first if later fields benefit from seeing those earlier fields' output. You have to test it because some times the results are surprising in directions you didn't expect.

XGrammar has an option somewhere to allow fields to appear in any order but I don't know if vLLM exposes it. There are some tradeoffs and limitations for allowing fields to show up in any order because there is some complexity in schema parsing like that.