Mary, I use Espoma Bulbtone and azomite when I plant the peonies. If I have bonemeal on hand, I will add that to the planting hole too. Then in spring when the pips poke through the soil, I apply the bulbtone again, 1-1.5 tsp per plant. I usually apply the bulbtones to new plants and those peonies that are slow growing. Those that are too vigorous, I don't fertilize. Miss America and White Cap grow too fast for me so they get no fertilizer.
I have never tried Superphospate on peonies. Though one year I used it on gladiolus bulbs and the bulbs got huge when I dug them up in the fall.
Celia, if it is any consolation, my YaeZakura tree did the same thing. Got two promising buds that midway stopped growing and became soft. Hopefully, this would mean that we get many nice flowers next year.