I didn't go through the Helicopter Training Next (HTN) pipeline so can't really comment on that. Advantage of going into Rucker with T-6 flying experience was primarily with formation flying - after learning how to fly fingertip with planes, flying 3-5 rotor disk separation with a Huey during the latter part of pilot training came about fairly easily. Downside of having a T-6 background, there was a lot of "unlearning" that had to happen, things like stick back vs stick forward on takeoff (you want to lean forward with a helicopter on takeoff to gain forward airspeed before you 'pop' up).
As far as helicopter jobs outside of the AF there're plenty - in the last few years several Majors and Lt Cols got picked up for airlines, one guy got picked up to fly down at McMurdo Station down in Antarctica, another guy got hired as a contractor to teach the students at Rucker, lots of government agencies are always looking for experienced helicopter pilots (think border patrol, FBI, National Park Service, things like that). Oil rig offshore transport is pretty big as well.