My primary Twitter account is also protected and, like you, I don't have to worry about the SPAM because I'm able to approve or deny access to my tweets, but the one I listed above is a general Twitter account and not protected and the SPAM is becoming quite annoying. I may have to protect it if it continues to get worse.
I have 2 accounts... This one is for my tech and video games news & I tweet about those type of things... Ronnie G... (@EvilMickWon) on Twitter follow & I'll follow back.
And this one is a more personal and entertaining account. I tweet about whatever's going on & such... Mick Lovin (@KoolMcLovin) on Twitter follow & I'll follow back.