There might be somebody who will respond to you with personal experiences (which I can't help with in this case), but I've used the TrailDEX map located on the website and zoomed in on the Chiricahuas. There's an option to "Find Springs".
Here's the link to my results, though you can zoom in or move to a more specific location and re-run the find function to narrow it down a little bit. http://hikearizona.com/location_g.php?QX=672
Of the 24 springs found, there are 8 where a spring report has been posted. I recommend reading all of the spring reports and you'll get a good feel for what you'll find. Make sure to note the time of year the spring report was generated.
There's a wealth of information on this site, and not all of it is easy to find unless you use the site a lot. Hopefully this feature helps answer some of your questions.
When you get back from your trip, please share a triplog with us, and add your own spring reports to help the next hikers out. I hope you have a great trip!