Sounds to me like it was improperly shimmed. I didn't really get the problem when I first read it, but the 153 tooth starter shouldn't fit on a 168 tooth flexplate (Well... without a big hammer, an angle grinder and lots of determination), and the 168 tooth starter won't even touch a 153. So, what you will need is a set of shims, and then make damn sure the starter pinion is NOT staying in mesh with the flexplate after the car starts!!! My car did this when I first put it together too, but I knew about the shims. You have to remember that this is an older GM product, not a modern Japanese car. NOTHING fits without a stack of shims in it somewhere! :lol:
As for how to shim, here's a tip: Most shims have one end that has the hole open at the tip. That is the side that goes towards the oil pan. This way, you only need remove the outer bolt, and loosen the inner one a bit. You can then slide in the shim with the starter's weight still supported by the bolt. All you have to do next is start the other bolt, then torque both of the bolts. Just be sure that you have both bolts started before you torque one down. it is the easiest way to align things. Also, you may have to shim it several times to get it right. That is why the package of shims comes with more than one. These are NOT precision parts either, they are meant to work with a fudge factor so that the parts did not have to be made too precisely.