By Drew’s account the snowbank already tastes good. Also it is a native Rubus allegheniensis cultivar, so crossing with other allegheniensis will only take it so far size wise. The Nettletons by all accounts appears to have nicely sized berries with very large drupelets, but tastes not so hot. The patent says they are Rubus fruticosus which means its supposed to be a European blackberry but in reality means they have no clue. The Nettelton would likely be the easiest cross to make and maintain flavor and size. But to get big berries is going to require outcrossing with a large drupelet or multiple drupelets cultivars, which are two different traits.
The problem with that is most commercial cultivars are x4 or larger polyloid’s and nettelton and Snowbank are normal 2x Diploid’s. That means to get fertile off spring you first have to double the chromosomes. Then you have to cross and back cross the offspring at least twice to ensure at least 4 sets of the gene for white get expressed or suppressed. And thats assuming one gene is at play. With any luck larger berries could result from chromosome doubling like how most triploid apples express larger fruit. Then all you need to do is select snowbank x nettelton seedlings for size and flavor first then double that plant.