Chris Moses mentioned speed and timing for instance. Like in some IT drills you ask some specific type of resistance or cooperation. But only in some kata do you specifically ask this type of cooperation (ok ok there's always some sort of cooperation but at least I try to get to a point where there's none). How many times do you perceive uke (and yourself too) switch gears during a kata sequence? I guess it's one pitfall of knowing in advance what's coming. At least I'm certainly guilty of some of that though I'm trying not to be.
First, very few lines of Aikido do what I would really consider kata, that is a very specific detailed COMPLETELY choreographed scenario for uke and nage. Aikido generally trains in a grey area between kata, oyowaza (applied technique) and randori (in the Judo sense, not multiple attackers). If people were actually doing kata, this would be easier because there would be a very specific way the attack was done every single time that would facilitate the study of that technique. But, like you point out, people change things up, attack differently, respond differently and (very unfortunately) take advantage of their knowledge of where the technique is going. That's not kata.
So how we train it, is actually to move more into a kata like relationship. Training partners DO request a particular kind of attack. We DO agree to the speed that we're going to work AND call each other on it when we leave the agreed parameters. It's common to hear people ask their partners if they want more pressure, or what kind of pressure they want (neutral, pulling, pushing, muscular, structure/frame based...). It also requires nage to be very introspective and critical of themselves. A common scenario with us is for nage to pull of a very respectable throw only to have them exclaim, "that sucked, I lost my frame in that transition..." or "crap, I blew that and got my shoulders involved..." This is even when the throw worked. That means using the litmus of, "did they fall down?" is no longer a high enough bar.
Certainly this can't be the only way you train, but I think this is the aspect of our training that directly addresses what you're asking.
If you're just trying to work the stuff into someone else's class, that gets more difficult. The responsibility for self introspection is even greater. If you're getting used to the sensations within your body, it should be pretty obvious if you're paying attention. I had a returning Aikido student in some of my Aikido classes last month. He was very difficult. He used to do aikido maybe 5-6 years ago, but had some health problems (including brain surgery). Guy was very strong, taller than me by a bit and had a good 50 lbs on me. So we're doing kokyu-ho at the end of class and he's pretty much just shoving me. On his fourth attempt, I switched from light structure/muscular resistance to almost entirely structure resistance and it took him about two minutes to finally get me off my center. His shoulders were having uncontrollable muscular contractions by the end and he was short of breath. So we switched and I worked on aiki-age using structure. He basically sat on my wrists and used all of the tricks he knew to get some "payback" as he put it... Here's the thing, he was incredibly difficult to do the technique (kokyu-ho/aiki-age) on. He was strong, being tricky, changing his grip... This went on for another couple minutes before I finally was able to pop him over. While it took both of us quite a while to accomplish the 'technique' (exercise really...) I was honestly very pleased. By the end my arms were not tired in the slightest, I had never experienced any muscular shaking, and had eventually been able to overcome his very substantial resistance. At the same time, he was so literally exhausted from the effort it had taken to resist me that he had to go to the edge of the mat and rest. He couldn't even continue doing any more kokyu ho. Certainly I would have preferred to go all Sagawa and laugh as I hurled his pathetic attempt to resist me across the mat (all the while telling Kimura he was an idiot and would never be able to train as hard as I could, ha ha ha ha!!!).
So, definitely room for improvement, but I was able to get very good feedback for myself.
Solo training means more than not having a partner.