In regards to "variations" during testing are you referring to oyo waza (applied techniques). Our testing is the same as yours then. I actually enjoy the inclusion of both applied techniques and knife defenses. It keeps training more interesting. If we only practiced basic kata and nothing else I think it would get pretty boring. Our group also practices Kokamishin so a lot of those techniques find their way into our "applied" curriculum. Interestingly a number of Kokamishin techniques are very similar to Aikido.
We never use the term oyo waza but applied techniques sounds very like variations. Don't get me wrong I think applied techniques and knife defenses are very important both to the art and self-defence; knife defence is one of my favourite things to do because I think it is so useful and it really tests your reactions and muscle memory. Perhaps I have not found the harmony and balance between them in myself. The month or so leading up to a grading is quite a stressful time just because there is so much to practice and sometimes when you don't have a regular uke it is hard to feel like you are making progress because you have to constantly adjust to a new body type/strength/agility/skill level etc. I think that is what has caused my training to suffer (if indeed it ever has suffered) the most not having a regular training partner.