I'm doing aikido since a bit more than two years, so we're more or same at the same level, and me too, I HATE ushiro ukemi, although I can do it (not very elegantly, but it's enough for me).
I just wanted to add two other things to Dalen's text:
It helps if you use the second leg, which you don't fold when going down in order to kick upwards. For one, it's an additional atemi to the person who brings you down
, and secondly, it gives you an impulse to roll back (kicking upwards-backwards, not upwards-forwards, obviously).
Secondly, there are a lot of techniques where you can escape ushiro ukemi. You can
a) spin out of it at the moment of being thrown and do mae ukemi, yoko ukemi or a strange thing like dorsal fall, which is something like yoko ukemi but more backwards. That works fine for kote gaeshi, shiho nage, tenshi nage, even the ura form of irimi nage, and it needs just a small adjustment of the direction of your body, mainly of head and shoulders in the forward or sideward direction. I don't know if I expressed it well, but it works. That's my preferred escape.
b) you can just do half of it until rolling onto your shoulders and then come back. That's what I do when a) doesn't work because my head is locked, uke blocks the escape way or I just don't manage. It has the inconvenient that it just ends in ushiro ukemi if the throw is really dynamic. But then you can escape it rolling from the shoulder to the side instead of doing the real ushiro ukemi.
c) when there is absolutely nothing to do, and you are brutally jerked backwards like in most forms of irimi nage omote, just do the fall on your back slapping with the arms to buffer it, and turn the head to your side in order not to fall onto it.
Then again, all these tricks don't save you from LEARNING ushiro ukemi, but at least you can escape it if you really fear it when being thrown. I don't know your prof's attitude to this issue - I know people who even encourage it and others who say that it's too risky, and you don't always have the opportunity to escape, so just stick to good old ushiro ukemi...
Best regards, and happy training!