Those wild variants and bughouse are fun to watch others play. It's beyond me how they can come back and play normal chess afterward. :-)
Here on Chess Tempo, where problems can be black to play or white to play on any given problem, I often wind up trying to checkmate the wrong king. Kind of like not knowing your left from your right.
I used to play those wild variants on ICC back in the day. My favorite was finding a very weak opponent and giving "Queen odds". Somehow beating someone without my queen gave me satisfaction. lol
As for trying to checkmate one's own king, I was kinda doing that for a while. Now, when the position loads, I go through a certain ritual. First I look to see which side is next to move, then I count down all of the pieces to see if there is a material equality. From there, I am usually pretty comfortable examining the simple tactical themes present in the position, then mixing & matching the themes as I try different continuations until I find the answer. It seems to work for me.