I agree that what the majors want to see is right-seat time in a (regional) jet.
Hey Javichu,
Watch this YouTube video:
“Inside Singapore Airlines”
https://www.youtube.com/watch?v=pKuGqKYk3pQ&t=1333s
Go to 29:06 and watch a young lad take his six-month checkride in a 777. Use this for motivation for when you are feeling frustrated. If he can do it then so can you!