Have you thought about using an actual sphere as a goal object?

You can assign an object/shape etc. as a "goal" for your particles to get to over time or with the aid of fields, etc.

So say you have an onmi emitter shat shoots-off 100 particles.
You can assign goal shape for them to form into after a certain amount of time has passed.

Check the help for details on using goals with your particle shapes

Good luck!