I had some outdoor first aid course a while ago and what stuck with me was the advice of a doctor who told me to simply gently massage the tick in a circular motion. Don’t drown it, don’t suffocate it (or it vomits into the wound). Just massage it with your finger in a circular motion until it lets go.
Didn’t have a chance to try it yet but he was a sound guy and sweared by it for many years.
Alea iacta est ("The die has been cast")