BTW, the casting numbers you gave (3970010) was used for SBC blocks with a 4.000" bore from 1969-1980, could be a 2 or 4 bolt main with the cubic inch of 302, 327, or 350. Look at the machined pad on the right side front of the engine just under the alternator. Look for a 2-3 letter code with a numeric serial number and we can get a better idea of what you have. More than likely the engine does not have a solid flat-tappet cam unless someone put it in there. Back when I was a younger man, it was believed that additives were required. It was also typical for people to run a heavier oil than required to keep up oil pressure (something that I was guilty of), but quality oils of today need no additives.
Most modern engines nowadays use 5W30, but a good quality 10W40 will work fine. I found a long time ago that it does not require a lot of oil pressure, but rather a good flow to all moving parts. I might think a bit differently if the engine was running extremely low oil pressure.