This is not me, this is what I have heard on here or youtube somewhere. I use damage and the specialist killstreak. What I have heard posted somewhere that when you max out the killstreak and get all the perks, you also get all the profenicies. So if you use damage, you also get range when your got all the kills. But it said if you you range, you do not get damage if you get the specialist rewards. Like I said I could be wrong, just hear say.
But I have used them all, and in the process of turning them all gold once again. In my opionion the AA12 is the hardest to use until you get damage or range. The single shot ones I usually run on a overkill class as my second primary to level those up. Just got done with the AA-12 over the double weapon xp time. So with that gun it took till about 400 kills to get it just above level 30. So back to your orignal question of how many kills, since that was double weapon xp time, I would say it would take roughly 600-700 kills to just get to 28 to unlock damage. Thats an estimate.
I use all the shotguns and if you are willing to do all the challenges for the different proficiencies & attachments it can go by some what fast. Levels 25 to max are the slowest. It sucks using the sites on a shotgun, so when I do I use them with the quick scoping technique (I can't do it with a sniper rifle, but i can with a shotgun...go figure). The Model, USAS & SPAS I use power. On the rest I use range. I find the range takes away from the in close accuracy and I lose kills that I would have gotten with power on instead. But at the same time with range you can get kills from a farther distance that you couldn't with power on. Shotguns are just too fun!
what makes the striker so popular is the fire rate and the fact that you can just spam the trigger and unload like 5 blasts in no time. I prefer the USAS with range as it already has great range for a shotty and with the range proficiency you will not have to hit em 4-5 times. once will usually do the trick. i know you like the feel of the striker but i assure you that if you take the time and play with the USAS until you get range, you will reap the rewards and be glad/proud you did. God doesn't just hand you a thunderbolt. He makes sure you are worthy and willing to earn it.
With awesome power comes awesome responsibility.