My hair does this with polyquats, too! It's a horrible feeling -- I remember thinking there was no way my hair would ever get back to normal, I was sure it was wrecked!

I have no advice other than to avoid the 'quats, sorry.

2c/3a, fine, low porosity.

Poo: Garnier Fructis Pure Clean (yes, it has a mild sulfate, but I have Teflon hair)
Co-wash: VO5 Kiwi Lime Clarifying Conditioner
LI: GVPCB or
Keratin Complex Vanilla Bean Deep Conditioner (nothing to do with keratin straightening, just a nice conditioner)
Style: KCCC + Pantene Curl Shaping Gel (winter) or LALSG (summer)
Dry: Diffuse or air dry, depends on my mood