You mentioned that you are printing Sport Tek jerseys. Their Posicharge versions are, as advertised, extremely resistant to dye migration.
At least in my experience, they do not require a special Poly ink. I used regular, cheap, Wilflex Low Bleed Streetfighter, and even added a little stretch additive and had no issues!
They even have a promotional video in which a printer uses plain old regular cotton white with no bleeding.
I'd still keep my eye on the temps, but I am a believer.