I was strictly a 91/135 background guy with around 6000 hours 3000 turbine PIC. I was not getting calls by any of the majors even though I worked very hard at getting my app squared away, gathering LOR’s from both UAL guys and non UAL guys, doing volunteering, job fairs etc. I then left corporate for a regional (because I knew most pilots were being hired by them or military and I wanted to be there) and as soon as I updated my applications I received two interview invites from major Carriers. My situation was a bit different though as I had large business jet international time so YMMV.