Starter Isn't Giving Sourdough Bread Enough Lift

Hi:  I'm loosely following Peter Rhienholt's Barm Starter recipe as found in his Crust & Crumb book and I've begun a new starter initially using Organic Rye Berries that I milled into flour and raisin water made by soaking 2 cups of organic Thompson seedless raisins in warm water for 15 minutes for day one, then, once I got bubble to appear converted this to a organic unbleached bread flour starter. I continued feeding the starter for the next 4 days and had, what I thought, was a pleasantly tart tasting, bubbling starter. However, when I began using the starter in my to make sourdough bread, now twice, I'm not getting the kind of lift in the loaves so that they rise more than 2 - 4 inches total and the center of the loaves are a bit moist.

I've slit the loaves with a lame, spritzed the oven with water, put a pan of water in the oven and baked the loaves in bread pans placed on top of my pizza stone, but still not enough lift to really give the kind of well formed loaf that I am looking for.

Any ideas???  Please share them.

Thanks, Ken