I do not fertilize my raspberries & they are still trying to take over( I water & get bigger berries).
I put compost out every Spring & early Fall, then mulch to keep water in & weeds out of my blackberries & strawberries.

The Oregon State method you referred to probably involves fairly fast-acting fertilizer, is intended for commercial farmers, and would work well.

For blackberries, a good dose of manure-containing mulch applied in late fall or early winter works fine for the rest of the year, can protect the ground from freezing in winter and drying out in summer.

Water becomes more important in late spring to early summer if your weather is dry then.