I'm sorry if the decision to close your previous thread has disappointed you.
We're happy to answer questions from prospective customers in the Pre-sales forum and we're happy to provide support via our other forums and our ticket system. Unfortunately we get a lot of people who are not licensed attempting to ask questions when they are not entitled to support and really it is only right we spend our time supporting our paying customers, where possible.
With this in mind, I can answer, yes, it is possible to construct search queries using GET instead of POST, but the response remains the same when it comes to how to do that. We can only support our customers who are entitled to support.
If you are acting in an official capacity on behalf of an XF customer, they are able to add you to their list of "Forum Users" in their Customer Account, at which point you're then able to post your query as if you were a customer in the appropriate forum, the XenForo Questions & Support forum.