My solution was to have Two Happ Super (8-Ways) as Joystick 1&2 plus the happs Mechanical Rotaries as Joystick 3&4 (Which look identical to the Happ 8-ways). I have no problems with Karate Champ using the dual 8-ways and of course Ikari works great using the Rotaries.
8-way joysticks drive me nuts in Karate Champ, though T-Sticks would be good probably, and they are easily switchable, plus they have a short stiff throw similar to the original Karate Champ joysticks. The problem with using them on a multipurpose control panel like the SlikStik is that they are too far away from each other, and if you put them as close together as they were on the real machine then that pretty much turns it into a dedicated dual joystick panel, because there is no room for buttons where they should be for single joystick games.
Your setup for games like Ikari Warriors sounds like you would be playing in a weird position, i.e. slightly right of center for player 1 and way right of center for player 2, which would irritate me as well.
Since the games I mentioned are some of my all-time favorites from the arcade, I am more picky about how I would would set up a machine for them than I would be if they were just some games that I thought were just OK and had never played much, if any of, in the arcade.
I think I'd need the original machines for the games that I really liked and played a lot of in the arcades to make me happy, then a general purpose MAME machine for everything else. At a bare minimum I would want:
1 fully functional original Punch-Out machine + 1 Super Punch-Out conversion kit.
1 Ikari Warriors machine
1 Karate Champ Vs. machine
2 general purpose MAME machines (one with a vertical monitor and 1 with a horizontal monitor)