Yep, absolutely, stirring is one way to get a creamier texture.
rennet amount and pH at adding rennet all matter. For the style you're making, you're adding rennet right away, correct? Then you need only a minimal amount, 1-2 drops per gallon, just as you have been adding. If you acidified the milk to 6.0-6.2 and then added rennet, it produces a different curd, one that can be firmer without losing a silky texture, provided that you drain at the correct pH of 4.5-4.7.
If you added more rennet at the onset, you would get a firmer more custard-like curd. Using less rennet at the onset would give you a more gentle curd that is more creamy.