So...what did you do? Picture please...

I see a lot of ZZ but I wouldn't ZZ because you are going to be doing a lot of stitching on the bias.... pucket time.
THE BLANET ST is much easier and more for giving. Just so you like it and I would use colors to match the sections.

If for some reason you use the invisable thread mak sure it is the pressable kind or it will melt away if you press.... I am not a big fan of the invisiable threads. You want a fun beach ball so colors or a blendable thread not a Varigated. Varigated thread is to much of a pattern where a blendable thread is uneven sections... like the Sulky Blendables are wonderful

And yes I would use the same thread in the bobbins, and you need to use some kind of a stablizer under the stitching. And unless you are a seasoned satian stitcher again I stress you are working on a bias edge... A loose ZZ is a better choice for you said they are fused down allso....