After spending ten minutes with the detangler cream soaking in my hair, I began to comb with my hair, from tip to root (very important - don't start from the root to tip!), combing downward. It took five to seven strokes in each area, and much of the time it hurt from the pulling. But it was all worth it to have my hair back again.
I'll keep this method in mind for next time, because there will always be a next time since I love the vintage sets.