You HAVE to use whichever flywheel fits your bellhousing, it's not a choice unless you swap bells. 157 tooth flywheels fit only 157 tooth bells, ditto for the 164 tooth. There is no such thing as a 160 tooth small block flywheel or bell.
I have had about 10 people, including the mechanic that I work with on my rebuilds tell me that there is no such thing as a 160 tooth - that is until I showed them - there IS such a beast, they WERE used in the early years.
The difference in tooth count between the 157 and 164 was due to the diameter difference of the flywheel itself, they both use the same starters and bendix gears. The only thing I can think of that might use a 160 tooth wheel could have been a 5 bolt bell. And these can only be used on pre 65, 5 bolt blocks. They do not bolt up to the later 65-up blocks.
Thanks for all of the info on this - I think we have found a solution - this gear ring is pressed on to the flexplate - we are going to try to press it off, flip it over and use the other side of the gears.