IMHO your fastest way to a Major is joining a regional the moment they will hire you, and joining a "reserve" big plane unit, Navy Hercs/C40, or Air Guard/Reserve take your pick of plane....As far as Navy reserve deployments, they are cake compared to active side. basically doing 1-4 3 week dets a year, and various other missions lasting 2-18 days, give or take. Lots of overwater flying involved. We have several prior helo pilots from all services flying doing basically what you are talking about, building Multi engine PIC time in an effort to one day join a major.