These are generally not suitable for sublimation printing. I would recommend pigment printing for this application. As of today I don't know if there are transfer papers for pigments aimed at the textile market. If they are they might provide a solution for you. The pigments must have a binder to attach them to the polyester filament so either a binder in the ink or one on the paper which transfers to the textile must be present.
Any help is appreciated.
Im told most inks like Sawgrass wont last outdoors.