7/16" is a fairly low nocking point for a split finger bow shot 3 under, or any traditional bow shot off the shelf. You didn't mention if you were shooting off the shelf or a rest? Bows using a rest sometimes take a lower nocking point.
I shoot 3 under, and have about 25 bows of different brands, some longbows, some recurves. Some are tillered for 3 under, some for split. All have been bare shaft tuned. All are shot off the shelf. Most of them have nock height of 5/8". Some have nock height of 1/2", and a very few have nock height of 3/4". I have bought some in the past that seemed to require a nock height of 7/8" or more, but I don't like that high of a nock height, so they didn't stay around long.
I have found that increasing the pressure on my index finger and decreasing pressure on my ring finger allows a lower nock height. I have also found that different arrows may tune to a different nock height, even arrows with close to the same weight and the same spine designation.