If the starer came from a discount autoparts store take back ans get one from a salvage yard if possible. I went through four starters in four days on this Chevy. They were the lifetime guaranteed starters from Oreillys. They are remans and don't fit no matter how shimming is done (at least in my case). I got a iron nose starter, rebuilt it myself and it's worked each and every time I've used it. Granted, I don't use it every day but the iron nose starters do not flex and are generally built correctly and won't warp over the years.
As for the iron shavings. Hopefully the rebuilders did at least this part right and used a starter gear that was somewhat softer than the ring gear. There is not supposed to be one spot that a 350 stops at every time it's shut down but that is not always the case especially if one cylinder has better compression the other seven. Might want to inspect each tooth (don't worry it's only 153 of them if you are lucky LOL) to see if even one is shaved. Have helper with breaker turn the engine over and have everything made safe so the engine has no possibility of firing. This includes removing every spark plug (makes it easier to turn it over slowly anyway).
The other thing that is of some importance is making certain that the wiring is in top shape to the starter. That battery cable can corrode inside over the years causing all kinds of problems. Just some things to check.
Good luck.
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