Another way of learning a piece "thoroughly" ?

Apart from nerves turning my fingers into sausages when I try to play for others, my brain seems to go on coffee break and I'm quite likely to get stuck in the middle with no idea how to get restarted.  I know this is because I've only learned it by "muscle memory" and anything that interferes with the flow (like missing with one hand or the other) is likely to result in a blank because my conscious brain kicks in, and "it"  hasn't learned it. (I find it totally amusing to contemplate having 2 brains inside my head that don't speak to each other - much more fun than the scientific description),  I've tried half heartedly to kick my conscious brain into action by learning things one hand at a time - and in fact have had some success with the left hand alone (plus singing so I know where I am), and for short sections needing to be worked out, the right hand alone while reading the score.  However it's totally tedious (ie not fun) and I am having a hard time making myself do it.

So a few weeks ago my guitar teacher gave me specific instructions to practice a piece at an unbelievably slow tempo.  Almost so slow you couldn't tell what was going on.   The intention being I would have time to  concentrate on all the things I don't do well (or at all), like actually hitting all the notes and making them truly legato.   However it had the serendipitous effect of making me think about what my hands were doing.  Indeed I find I have learned the part I was working on quite well.  Admittedly this is just a small sample, but it does offer another way of perhaps getting a piece lodged properly in both 'parts' of the brain.  I don't know if you've ever come across the effect that when you try to play something a lot slower than normal, you "forget" what you were supposed to be doing and get lost. I certainly have.  I'm hypothesizing that at very slow speeds,  the muscle memory sequence is disrupted and your conscious brain has to kick in instead.

Anyway I'm excited to try it - particularly on some pieces I ought to be able to play well, but am prone to "forgetting" in the middle.