There's a lot of important reflection in your post. I'll start at the end.

Intellectually, I know the only way to get better is to do it. What I have to figure out, though, is how to reduce my frustration levels to a manageable level, since right now that side tends to win out. I also kind of psyche myself out, where I expect frustration to be the only result, so don't bother trying... I know some of you on here do various creative pursuits, so how do y'all cope with this?

It is an inevitable truth that you have to accept when it comes to art. The process of mastering anything is unavoidably full of frustration: a finished piece is never as good as what you initially imagined, things always take longer than you expect, there's often no-one around to just tell you what you need to do to improve. In the long run, it's likely that you'll quite often find yourself periods of frustration on various levels of the process. There's a great excerpt from the book 'Infinite Jest' that that touches on this:

"...His point is that progress towards genuine Show-caliber mastery is slow, frustrating, humbling. A question of less talent than temperament... You proceed toward mastery through a series of plateaus, so there's like radical improvement up to a certain plateau and then what looks like a stall, on the plateau, with the only way to get off one of the plateaus and climb up to the next one up ahead is with a whole lot of frustrating mindless repetitive practice and patience and hanging in there." Infinite Jest - David Foster Wallace (Full Excerpt)

Ultimately, the only way through this frustration is will power and trust in the process. This isn't the answer people generally like to hear, but it's the truth. And honestly, the frustration never gets that much easier. But you you will get used to feeling frustrated and start to see it not as burden but as catalyst for action. Because if you're frustrated it at least means you know something 'is wrong, which means your on the first step improving and getting better.

There is one thing that makes it a bit easier though: discipline. Sit down every day (or whatever you schedule) and do some drawing. Make it purposeful drawing too; coming to a blank piece of paper with no impetus is often fatal to the process. So before you sit down, known what it is you're going to, even if it's just a rough idea. Today you're going to draw a flower; tomorrow you're going to practice your shading; the next day you're just going to use pens, whatever; maybe you liked the flower and the shading practice gave you new ideas, so you revisit and revise the flower. Keep the momentum going and keep completing pieces. Soon enough you'll feel compelled to work regardless of frustration.

In regards to your Kung Fu vs. drawing issue, I think it may be that you're relating to your Kung Fu development on a micro level (i.e. individual techniques) and drawing on a macro level (i.e. a complete picture).

In my limited martial arts experience, whenever I touched hands with a senior student or teacher, I was directly practising a singular technique. A kick, punch, or block. I not only got real-time feedback of my own attempts, but got to feel what it was like to be on the receiving end of my partner's higher mastery of the technique. This adds up to create a highly efficient and effective learning environment. On the other hand, with drawing it seems like you're looking at a great artist's complete picture, comparing it your own, and getting demoralised. This is like watching a black belt perfectly execute their grading routine after you've just managed your first complete run through of a white belt routine. Then the black belt turns to you and says "good luck, kid." Do you see what I'm getting at?

With kung fu it's more a question of degree...that is, a technique may work more or less, but there are ways to refine it

It's essentially the same with drawing, or any art. Even humanity's greatest masterpieces can be broken down into a collection of techniques. Use of shading, contrast, colour, line thickness, etc. And these things can always be refined. So whilst it's unavoidable that you'll judge your drawing as complete picture, remember to also analyse it from the a technique level. Maybe you don't like the drawing overall, but you can see you did the shading really well. Or perhaps you do like the picture overall, but you feel your use of colour let you down. These are the sort things that you can then take to your next piece and improve upon or combine in different ways. Practice that technique specifically like you would a punch in Kung Fu if it really needs work. Also do this for the artist's work who you admire. Why do you like it? What techniques are they using and how? Then steal their ideas and try them yourself.

In my own compositions about half a year ago, I identified that my sound design wasn't as good as I wanted it to be. I have been composing for 10 years and have produced a good amount of tracks, so it wasn't one of those things that was just going to improve on it's own. So I sat down and practiced it specifically. I found a in depth online course to help me along and made sure that I found ways to use my new skills in my work. Now, 6 months later, my sound design is a hell of a lot better. It's still not where I want it to be, but it's getting there.

I think this is the kind of approach you need to have.

With drawing, if I'm genuinely unhappy with what I've done, then why am I doing it? It's not really about showing off or being embarassed about where I am, but more that some theoretical future improvement is just too abstract

That's art for you. With Kung Fu there's a structural progression and concrete, defined things you need to do to reach the peak of that progression. With art, there is none of that and you have to decide what your end goal is and then figure out your own steps to get there. I can relate to you on this. I've always felt that I've been working towards some ideal in my head. Yet that ideal is obscured and I can only discover what it looks like by creating things which align to. Unfortunately, I think this is again just the way it is. But remember, just because you're unhappy with what you've done, it doesn't mean that it wasn't beneficial to do.

So when it comes down it, you answered your own question. The solution is to do hard work and lots of it. In the moment, the work is often far from as enjoyable or as fulfilling as you might like. Stick with it for the long run, and it will be. It's great you're willing to do it, but you also need to be willing to put up with all the hurdles and hardship along the way.