Okay, when you say "another block", am I correct to believe that you swapped out one motor and dropped another motor in its place that had the same casting number on it? First thing that comes to mind is in connection with that number itself. Those castings came in both 2 and 4 bolt configurations. Had that number casting come into my possession and went to my Cars and Parts reference manual to learn what it had come from.
Quoting that specific page here, "3970010 first appeared as a casting number in 1969, as a 350 CID installed in Corvettes. It also has been used in 69 Camaros in a 302 version, 69-79 trucks, 69-79 B, G, and F bodies, and 70-72 Vettes with varying horsepower ratings." For those versions for cars and trucks listed as being 350 CID used between 69 and 79, there were both 2 and 4 bolt versions that used the same casting number. Where I am going with this is that unless you pulled the pan to take a peek at the bottom end, you have no real way of knowing what version, 2 or 4 bolt, you have.
The block number itself is of no help; it has been used in too many applications and continues to appear as a replacement service number if you order from the dealer. The only possibility that could help you is the casting date, which should tell you the year and month that the block came out of the foundry. Typically, back then, for example, if a block was casted in, say 1970 for example, it would go out to the yard and sat for a year or two to season. Then it would be brought in for final machining. So that 70 casting date would be on an engine installed into a 71 or 72 vehicle.
With all these variations, more than one version of the starter motor got used as well. Just a quick peek at that section showed me a page and a half of numbers for starters used between 69 and 79. With all this in mind, it could be your starter has the wrong Bendix housing on it meaning that the mounting bolts are just enough out of alignment that while it worked with your old motor and bolts up to your new one, the bolt holes in the replacement motor and those in the snout casting are situated just differently enough with respect to each other that the starter mis-aligns. Sounds like you may be in for a trip to the salvage yard or pickers to do some comparison shopping for another starter.
