So my odd morning schedule won't hurt anything regarding recall? Because a guy I was reading on here, Sageous, kept stressing that working on memory was key to attaining more than very low levels of lucidity.
The fact that you wake up and go back to sleep doesn't need to be a issue. For example, when I have these awakenings in the middle of the night, I quickly use an voice recorder to point out a quick picture of the dream, which I can complete later when I get up. You can also write down a few keywords and go back to sleep without that even hurting your recall. What Sageous wants to stress regarding memory is that you won't be able to achieve proper lucidity if you can't develop good enough memory to locate yourself in "time and space". This is helpful even for dream recall, which translate into being able to quickly turn into your last memories when you wake up. For specific lucidity, picture memory as a solid backup: you know that you just went to sleep, and now you're walking in the streets of some random place. Another type of memory is prospective memory, which relates to the ability of remembering future intentions: especially useful in order to carry on intentions in your dream.

Also, you said to try and get into the habit of Reality Checks/Awareness Exercises, but he specifically stated not to get into the habit and to change it up, otherwise you might just dream you did it right in the dream (Or something)
Both of us are right. I was actually a beginner in that thread and you can trust that even with more experience under my belt I still highly recommend you to follow the ideas presented there. Sageous is someone who developed his lucid dreaming skills without the nowadays "talk" that you see in concepts like reality checks, techniques, tricks, etc, so much of his talk may seem different from more "modern" lucid dreamers. In the end, the essence is the same, but he presents it without masking it up, which some people (me included) prefer, but this information sometimes doesn't seem very clear for people asking for advice ^^

Anyway, regarding reality checks and awareness: they are key to your lucidity, but you should not do them as a mechanical action. What sageous means by "not get into the habit" is don't assume that a reality check is a simple action that you perform loads of times a day. It's actually an introspective moment in which you question the reality around you. This questioning and awareness of yourself and the universe is what builds the core of lucidity. A reality check can simply be trying to recall what you were doing 15 minutes ago like Sageous mentions. Others prefer other actions, like I like to look at my hand in order to abstract from the outside world and question myself. In the end, we are all doing the same: becoming aware.

Until your reality checks become a second nature habit, you'll have to consciously perform them. At some point (takes some time), they'll will come much more easily and spontaneously, but you must never assume them as mindless actions.

I hope I cleared your doubts a bit better now. Despite that, I'll try and see if Sageous sees this thread, as he will for sure be able to explain his speech much better than myself