This is definitely the way to start. The bottom line is: promoters for these type of shows are trying to pack the house so they don't lose money. if you're busting your ass playing lots of shows, it shows that you're hardworking and theoretically can draw a crowd. That's way more important than a slick press kit, good recording or well written email. More often than not, the hardest working bands who play out regularly are the ones who get those shows and for good reason.
In my opinion, the best way to get "high profile gigs" is to get in good with the promoters in your area. They're the ones bringing those shows there so why not go to the source? Aside from the importance of doing it yourself and having fun playing with out of town bands, booking your own out of town bands makes you look way more legit to promoters and can help create a good working relationship with them. It may start where a promoter says "here's this small show someone wants to play here, do you think you guys could book it because i'm too busy" but if you do a good job there, they might see you as a band they can rely on to open up a bigger more important show.
Also, if possible, always try to deal with them in person. You have to remember, if a promoter is putting on big shows, they're probably getting a ton of emails/facebook messages/texts/phone calls from bands just like yours wanting to play them. Those are super easy to ignore or lose. From personal experience in playing shows, the best way to get something done is to do it in person. By putting a face on your band, you make yourself more memorable than the tons of bands who didn't. You also show that you're confident enough in your band's skills to put a face to it. More importantly, putting a face to your band shows that you're willing to take responsibility for your band rather than hiding behind a screen name or facebook account. All of that is pretty important to a promoter.