GA Flight Instructor reported a near miss with another aircraft while conducting maneuvers on a training flight in a practice area. Both aircraft performed maneuvers to provide separation between the aircraft.

Narrative

The flight started at BJC as a ASEL commercial check ride training flight to practice the maneuvers listed in the ACS. The airspace around BJC; EIK; LMO; BDU; GXY is congested with many flight school students so some unofficial practice boxes have been established by flight schools as well as a practice area frequency.My 3rd maneuver practiced was a series of chandelles which took me to about 9500; just below the 10;000 bravo shelf; which is when I typically perform a steep spiral to descend to a better altitude for additional maneuvers. In the period between ending the last chendelle and beginning the spiral; I check ADS-B traffic on my iPad an noted other aircraft in the general area but no aircraft in my direct vicinity nor heading towards me. I then made a radio call on the practice area frequency to declare my intentions; then performed shallow bank turns before entering the spiral to the left; starting on a 180 heading.About 270 degrees into the first spiral; I see a turboprop banking away in a steep climb at roughly the same altitude and about 500 feet horizontal distance. At that time I determined that the best evasive maneuver for my airplane was to continue in the steep spiral. While checking the ADS-B traffic I believe I assumed the traffic in the general area was similar performance training aircraft that would not change heading and altitude abruptly and were likely aware of the practice boxes and listening on the practice frequency. During the 20 seconds sequence of checking ADS-B traffic; making a radio call; visually looking for traffic and setting up for the maneuver; the 2nd aircraft changed direction and began a rapid climb in my direction. I am not sure if the 2nd aircraft was flying on an IFR flight plan but if they were it is possible that ATC could have helped them navigate the congested training area. I am not sure if the 2nd aircraft was aware of the unofficial practice area frequency; but if they were listening they would have heard me declare who; where and what. I could have done an additional glance at ADS-B traffic prior to entering the steep spiral and may have noticed the 2nd plane was moving much faster than other GA training aircraft in the general area and had changed heading; at which point I would have canceled the maneuver. I could have also utilized the dual coms and audio panel to monitor CTAF at EIK and could have possibly heard the 2nd aircraft's who; where; what; if those calls were made on the EIK CTAF.