Helicopter pilot reported during final approach decided to go around and break off their approach. As they made their turn; another aircraft that was behind them on approach broke off their approach and ended up turning towards them nearly causing a near midair collision.

Narrative

Had a near miss with a plane down at SUW today. I had to make a very evasive maneuver within 500 ft of horizontal separation I am right traffic for 32; we had Aircraft Z left traffic 32; we are both doing patterns. Aircraft Y makes a call '10 southeast for straight in 32' and he sounded very old and kind of spaced out on the radio.Eventually I am 2 mile final 32; he is 5 mile final 32 behind us; and Aircraft Z left downwind for 32. We are doing a steep approach and taking time to get down to the rwy; I decide we should go around and break off approach since this guy is probably getting close behind us and he is full stop. We make a call and side step north and start climbing; around 1200 MSL; and start to enter a left downwind for 22 (switching rwys to avoid fixed wing traffic). As we are making our turn we end up nose to nose within 500 ft of Aircraft Y going southbound to cross rwy 32 (the plane that originally was on final behind us) I make a hard left turn to avoid him then right turn to get around him. The plane crossed midfield then left downwind and landed rwy 32. We continued and landed rwy 22; Aircraft Z made a turn to the north and 360 then entered rwy 32 The plane was established on final for 32; and had broken off his approach (turned north) and decided to cross midfield 32 below pattern altitude and ended up on a collision course with both helicopters all without making a radio call up until he was crossing rwy 32. Last call he made was 5 mile final rwy 32. I can take some blame as I probably should have flown straight out and entered right traffic for rwy 22 but I was trying to facilitate proper separation as I was worried he would have to go around and be right behind us going faster than us. He was not supposed to be there and I cannot think of why he maneuvered the way he did.