Motocross.
Honestly I would be interested in competition shooting. I have a Browning A-bolt 7mm Rem Mag I used to hunt elk with. At this time I don't have plans to hunt with it again (more interested in black powder) but still enjoy shooting it. Competition shooting sounds like a good time.
Consider primitive biathalons. Wooden snowshoes and PRB/open sighted ML guns. Some offer an inline class of competition.
It's lots of fun and you'll meet some great people.
Typical course is ca. 10 shooting sites, offhand at ca 50 yd, 2-3 miles long. 3 shots at each site at ca. 3 X 3 targets, hit or miss.
Score based on time and hits.
They also include "markmanship" contests. No running, off hand shooting. Smallest group wins.
The last one I attended ("markmanship" contests) was won by a man with a homemade flintlock in the PRB class. The guy who won the scoped inline class would have placed 7th or 8th in the PRB class (traditional ML open sights).