I had some success with my last sourdough installment. I just "got" why Reinhart makes a near-50% hydration starter from the barm. Quick explanation: yeast want something wet and warm; acetic bacteria want something cold and dense. By taking a ripe 100% starter (barm, really) and making a 50% hydration starter, and then allowing that starter to double before throwing it in the fridge, Reinhart gets to have his cake and eat it too. The 100% starter and doubling time allow for the yeast to reproduce enough to give the starter some leavening power, but the cool environment and its low hydration level allow the acetic bacteria to catchup during the cool fermentation. So, stage one, make sure your starter can raise bread. Stage two, make sure your starter contributes to the bread's sour flavor. Makes sense and is easier than the two starter method (which is, admittedly, something I am still learning).

Recipe (yet another adaption from Reinhart)

Starter (two stages)

Starter Stage One
4oz 100% hydration starter
4 oz bread flour
.5 oz rye flour
1 oz water (luke warm)

Starter Stage Two
4 oz bread flour
.5 oz rye flour
2 oz water (luke warm)

Dough (desired dough temperature is 72-76)
starter
18 oz bread flour
2.25 oz rye flour
.5 oz salt
12 oz water (90 degrees)

Mix together stage one starter ingredients. Knead to fully incorporate and reach a medium to medium-low level of gluten development. Allow the starter to double, then put in fridge for at least 12 hours.

Take starter out of fridge approximately one hour before use. Mix together stage one starter with stage two ingredients. Knead to fully incorporate and reach a medium to medium-low level of gluten development. Allow dough to rise for 3-4 hours (may not necessary double, but will come close). Put starter back in fridge.

Remove starter one hour before use. Mix 16 oz of starter with dough ingredients. Knead until you achieve a medium to medium low level of gluten development. Allow the dough to rise for 4 hours at room temperature, with stretch and folds after 50 and 100 minutes. My dough rose considerably, but did not double.

Divide dough into two, shape into boules. Allow for a 60-90 minute proof, then retard the loaves over night.

I baked the loaves some 6-7 hours later, but you probably have more time if you want to stretch it out. Pre-heat the oven to 500 degrees, prepare for steam baking. Put the loaves in the oven straight out of the fridge, steam for 5-9 minutes (I turn down the oven temp after the first 5 minutes because I steam less regularly after that, up to your method though). Rotate loaves, bake until brown crust is achieved.

Flavor is tangy, but not overly sour. I had one blowout, unfortunately, but the flavor was nice and complex for both loaves.