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Not myself,but a few years ago the city of Timmins had a bad nuisance lynx problem.
The Timmins Fur Council stepped up to the plate and caged and re located about half a dozen lynx.
Timmins Fur Council is a very active council in the community and they do lots of volunteer work all year long,from transplanting fish,maintaining canoe portages and trails,and garbage pick up at illegal dumping sites outside the city,and lots of other stuff like search and rescue etc.
They also hold a hugely successful wildlife dinner annually to raise funds for all their community work.The tickets sell out in a very short time each year.

One time I was on call for "resolving" the potential escape of a giraffe or an elephant from a traveling circus at a military base.

I got a call to an apartment complex that I do regularly for raccoons and squirrels. They had noise in the attic of one of the buildings and I went up the ladder and the rodent was waiting for me right by the hatch. I swept him into a cage and wasn't sure if it was a flying squirrel or what? So I stopped at a large pet shop on the way home and they identified the culprit as a sugar glider. I figured the little guy was tired from that long trip from Australia. The owner eventually heard about my capture and came and got him.

I can assure you that a flying squirrel would not sit still while you swept him into a trap, lol.

Weirdest animal? Probably chickens that were dropped off at a rural customers house. I'm ok without catching giraffes, elephants, bison and the like.

A "zole" is the strangest for me. Lol

Wood duck in a basement, actually had it happen twice.

Limestone, at that point I had never even seen a flyer, so I would never had known. Which is quite different than removing over 50 flying squirrels from one residence, which we did years later! I also had to jump up to net a wood duck that was flying through a guys living room. I'll bet he's got doors on his fireplace now! Cathedral ceilings are great if you're a duck!

African porcupine, no joke

A friend of mine who also does nuisance wildlife control had to remove an alligator out of a water treatment facility . In PA .

Rarest natives here. Weasel, mink, bobcat, muskrat in that order though bob kitties are common they rarely cause problems the others are just uncommon.