Pilot reported a near miss with a military aircraft in special use airspace while properly orbiting in accordance with a published Notam. The pilot and the other aircraft maneuvered to avoid a collision.

Narrative

At approximately XA00 and XA30 Aircraft X had two near midairs with Aircraft Y. We think it was the same aircraft both times. Aircraft X is a Twin-engine aircraft based at S52. On Day 0 we were conducting operations as NOTAMed.Both incidents occurred at 6000msl (2500agl) 3nm northeast of S52 at in the Okanogan MOA B.During the first incident at 10am Aircraft X and Aircraft Y were co-altitude within less than 500 yards of horizontal separation. Each Aircraft made right turns to avoid a head-on collision. Aircraft X was orbiting the area with a NW heading; Aircraft Y was heading SE when the near miss occurred. We received an aural TCAS traffic alert at the same time we visually detected the aircraft at our 11 o'clock and had less than a few seconds to react to avoid collision.The Second incident occurred approximately 30 minutes later. This time Aircraft Y saw us first and rapidly climbed and turned left to avoid. We did not need to take any evasive actionsWe were in our NOTAMed area making calls on S52 CTAF (122.8) Our other radios were up VHF guard and other frequencies. After the first incident; we attempted to contact Aircraft Y on CTAF 122.8 and 121.5 with no joy. We were orbiting the area at 6000msl. During the second Aircraft Y incursion at XA00; the individuals on the ground were conducting a helicopter mission. Once we landed; I contacted ZZZ Center to report the incident and submitted a NMAC per their guidance.Due to a previous incident; there is a process in place between two organizations to deconflict our operations and MOA traffic. This process includes the area of operation and operations being NOTAMed daily and the organizations coordinating. However; we need to improve real time deconfliction by having military traffic transiting the S52 area monitor the CTAF and make calls in the blind when within 10nm of S52. All our areas of operation are within 10 miles of S52.