@ OP,
I think your strategy is more likely to be detrimental than beneficial. I usually do the opposite, not allow myself to play a civ within 8 games of the previous time I played that civ. The reason is that you become too acclimated to the advantages that civ grants you, and need to re-learn how to do without it. Examples:
-You play numerous games as the Celts or Ethiopians, then move to any other civ and need to relearn how to play without first picks at religious beliefs, or even relearn how to play without founding a religion at all.
-You play numerous games as the Babylonians or Mayans, and need to relearn how to play without a very early and compounding tech lead.
-You play numerous games as the Carthaginians or Arabians, then find yourself trying other civs only to have your early economy crippled.
-While the previous examples all dealt with top-tier civs, the rationale also applies to lower-tier civs. As the Ottomans, you get used to being "bailed out" with gunpowder, turning the tables on all the civs who were picking on you. Become too accustomed to this, and then try someone else to find that you don't have that "lifeline."