Hi, Carelyn,
Welcome to the forum!
Don't have any suggestions for you, but I had the same problem, too. Couldn't outsmart my sphere mold either. I used heavy-duty rubber bands to hold the mold together, used an injector to fill the molds, and the soap still leaked sideways. It seemed the soap went everywhere except where I wanted it to!
I'd try to fill one sphere and the one next to it would start to fill, and very few of the spheres would fill all the way before the soap started leaking out the sides.
I thought about making half-spheres, popping them out and pouring more soap into the bottom mold, and then setting the finished half-spheres on top of the hot, just-poured spheres to see if they'd adhere to each other to make a complete sphere.
Anyway, I'm wondering what I did wrong, too, and would appreciate any tips!