Eric, your tree is revealing things to you as I'd mentioned. You just need to know how to interpret the message. What you saw as the bow leaned one way right away but then began to straighten/balance itself was 'normal'.
When you first put a tiny bit of pressure on the string, you are doing so from above the bow's center... (the center you would find equadistant from the tips). This causes the bow to begin tipping right off the get-go, and then as the relative strength of the limbs comes into play, the balance point shifts from the static to dynamic. It is the dynamic balance at full draw we seek.
This transition takes place under the bow hand and varies in dergree dependent on design, grip, and relative limb strength.
This static to dynamic transition is much more harsh on symmetrical bows where the string is pulled from even farther above the static center. Non-symmetrical bows, as you're working on, have a smaller, more gentle shift to accomplish and do it earlier in the draw.
Do NOT tiller to a predetermined tiller measurement like Roy said. You are on the right track and I have high hopes for you and your bows
My advice is to tiller it out seeking balance, either by way of the piviting cradle, or if it freaks you out too much, switch to the stationary cradle and use the perpendicular fulcrum travel to balance it. Then go back to the piviting cradle to see how ya did.
If your tree is set up right and you tiller for limb harmony, that sucker will feel perfect in your hands the very first time you draw it... tiller measurements be danged... I promise.