how do you recommend continuing and how do you manage the axis of rotation in your irimi nage?
I suspect your problem might not be in the steps but in the timing of them, and possibly in getting off your own center line as well.
After the first 180 degree turn, it's very very common to let uke continue a little bit too far along the turn before attempting to throw. Then the solution to that is sought in turning even further, but that leads to the kinds of problems you describe.
Try throwing uke a little bit earlier, even a bit too early for where you feel you should throw. If you time it right, ukes feet are still travelling forwards under your throwing arm and uke throws themselves.
The other thing to pay attention to is not letting your front hand get past your center line. If you do the kind of iriminage where uke's head is on your shoulder, that hand obviously is a little bit on the side of that. But your front hand can be more in the center. If you let it travel too far aside it will be hard to reverse direction for the throw regardless of how many times you turn.