I took lessons until I was about 16 years old.

I would like to get back into it, now at almost-40. I am frustrated in the loss of skills, and what's worse, there are certain fundamentals that I just never really learned well. Consequently, my velocity is quite bad, and even some simple scales I'm not really able to execute evenly. Part of that is a terrible piano, but the great news is that this is going to be rectified shortly (SO EXCITED!) What never went away was my general craving of it, but frustration, and lack of access to a piano that worked properly worked against that. I can lose hours in front of piano when I get to one I like, so it's still a part of me and getting a piano is the first step in finally respecting that and doing something positive about it.

All my expression and general musicality is still there. I just sort of sadly gloss over runs and other technical elements of sonatas and pieces I love. So I would love to sort of connect the dots and undertake a broad technical tune-up of my skills, and in some cases simply learn it for the first time now that I'm not 12 and fighting my teacher over just how important those boring exercises in Pischna are. Except now I don't have the ability to even teach myself without researching into it. Start slow, start small? What am I aiming for?

So you see the problem: while certain things probably need to be pulled back to a very basic level, certain other things are very easy for me. And I really don't know how to address that in a plan.

I think I need to think through a pedagogic approach here, either self-directed or with a teacher, and was hoping for some kind of input on how to go about that as an adult.

Any advice would be welcome!

Well, since you seem to indicate that a teacher is possible ... the only thing you need to do is find a good teacher that you can develop a relationship with and you are done. You just do what the teacher tells you to do and you're good to go.

And just in case I wasn't clear ... since a teacher is a possibility ... forget about self-directed, for any reason. Just find that teacher.

I also strongly recommend trying to find a good teacher who works well with adult students. When I returned to piano after my childhood studies, I was still interested primarily in classical music. Getting a teacher right away (and having the luck to get a really good one) was the best decision I made. Of course, if your ambitions focus on other musical genres, then other approaches might recommend themselves.

No, it would be returning to traditional classical study. I might see what I can brush up on for 6 months or so without a teacher. Right now, I've got two kids taking piano, and one of them studies violin as a primary instrument. So I'm kind of neck deep in teachers and after one teacher retired and the other really wasn't a great match with my daughter and I had to figure out a way to part ways after four years, I am scared of making a mistake, and weary of the task of researching, interviewing and finding music teachers.

I will say that my ballet teacher's first profession was as a pianist, and she does teach piano as well, which I wish I had known before I hired the teacher we now have. She is very good at teaching ballet, with a rigorous high standard, and I'm sure she would be interested in adding an adult student. I just don't know if I can handle another hour per week of a very stern Russian lady yelling at me to repeat it again, this time without the stupid mistake.

When I found my way to the piano, after having been in organ classes as a kid and then having paused with any keyboard instrument for 20 years, I found it for myself most useful to take advantage of the skills which I as an adult surprisingly discovered to have, but for sure haven´t got access to as a kid: I can hear myself playing. As a kid my feelings have been a mixture of what it feels to press the keys, feels to concentrate on the sheet, feels to discover the joy of playing and feel of what enters the ears, all at the same time. The result was sounding as a kid sounds: not mature.
Today, if having a good day, I can really manage to only allow the feel from the ears to reach my brain, while I filter out the other senses. Like this I get a much better expression - after 20 years without practicing. I re-work through all the beginners excercises again, and through raw beginners 'repertoire', although I at the same time could also work right away again on advanced level pieces (what I also do ;-) ).
Take your time and experience the difference, how you as an adult can approach the piano again, different then you might have done it as a kid. Discovering this can quickly get you up and runing again, in a very satisfying way.
Just my experience.

Yelling shouldn't be part of any lessons I think! Why don't you just ask the ballet teacher for some trial lessons. Then you can see how it works out for you.