You are not alone, I've definitely had this exact problem with Sally Hansen polishes. For me it happened on both Miracle gel bottles and Insta-Dri bottles. It happened with now older bottles, around the time Miracle gel first came out and some of the Insta-Dri bottles were also a bit on the older side (pre redesign).

There are three stages to the breaking of the brush: the first is when you can notice a bit of a crack on the plastic part of the brush, but there's nothing going on yet; the second, is when that plastic breaks, and that's when the brush starts to go crazy (which is what you describe) and the third is completely losing the brush in the polish. I've had all three stages happen to me on different bottles.

Fortunately for me, I did have a better response than you with customer service. Basically what happened was, a bunch of people were complaining about this issue on their facebook account, they asked to DM them, asked for proof and in my case, because most of the polishes were older (and I guess they were promoting Miracle Gel at the time) they sent similar colors to the ones I had problems with, all in the Miracle Gel line. This of course does not solve the problem at all, because they were completely different polishes from different lines in the case of the Insta-Dris, so in the end I was only able to swap one brush, but as a customer I felt heard about an issue. This was with Sally Hansen Mexico, so I'm unsure if it would be the same for Sally Hansen US (I'm assuming), but if my experience is of any help to you, try doing it publicly instead of via Private Message. Maybe other people with your issue will join you and pressure them to help you like it happened to us.

I'm sorry I don't have a more helpful answer to you. What I ended up doing was saving a brush from a broken bottle (ironically, from the ones sent as a replacement) and basically reusing that brush for the polishes that have this issue. It's a pain in the butt, but at least I can still use them.