For whatever reason, cycling through the rewards cards and the 0% teaser cards has never really had much impact on my credit scores. I expected it to, but it never really moved the actual number much in either direction. I'm usually teasing $10-20k at a given time and working on 2-3 travel rewards cards for sign-up bonus purposes. (Only things I really use are SPG Amex and Marriott Visa.)

In about a year, we will be moving and applying for a larger mortgage. I'll probably clean everything up a few months in advance of that - go in with zero debt and only 2-3 open CC accounts - but I don't expect a magical jump in the credit score.