What you did was the "figure-8" method, which is designed to avoid a jibe, but does get you pretty far from "Oscar" before you start heading back to him.
An alternative, if it's not too windy to jibe, is the "quick-stop" method, where you head upwind immediately, then circle around Oscar, jibe in mid-circle, then head up from below to get him. This method reportedly works better with a life sling trailed astern, it closes in on Oscar as you round him, and the whole thing keeps you closer to Oscar in the first place.
I teach sometimes on either Flying Scots, or on Beneteau 25s, and try to have the students try both methods.
Here's a good article on both:
Crew Overboard Techniques