How to get my ships to actually hold position.

Don't forget the guarding a warp point problem... set up a nice formation around the warp point, and every time an enemy ship enters, your ships scatter to useless positions. Having to turn off automove every time is fine (but tedious), but it makes non-tactical combat useless.

Or just as annoying, the automove while chasing (optimal firing) makes your ships turn (and slow) just when the get in weapons range of the enemy... instead of reasonably trying to overshoot their position.

Or just as annoying, I had a ship set to "don't get hurt" and it ran to the edge of the map and then turned, and got blasted by pursuing enemy ships instead of escaping.

Actually both of these are things that can be easily modified in the strategy you have assigned to those ships. They are under your control.

For the first, set the ship to a strategy that specifies short range, instead of optimal/medium. I don't have the numbers, but the definitions of "point blank", "short", "medium", and "long" range appear to be hard coded values and have nothing to do with the actual range of the weapons you may be using.

For the second example you cite, the ship is most likely doing what its programmed strategy specifies. Check the retreat settings. It sounds like you have it set to stay in the sector unless your fleet has been defeated, which would keep it from fully leaving.

Really? Under my control? How do I change a ship's strategy without retrofitting it or putting it in a fleet? How do I change a ship/fleet strategy during combat?

Setting all my ships to point blank and watching them die attacking a planet, just so they could properly chase down fleeing ships & fighters afterward doesn't sounds like control to me.

Changing ship strategies without refitting is easy.
To change ship strategy, go to the ship design screen.
Just below the "Make Obsolete" button is a "Set Strategy" button.
It allows you to change the strategy of the selected ship/base/unit design without needing to refit/edit the design.

But... give me a "Set Strategy" button in the ship controls for tactical combat... and on the pre-combat screen for strategic combat.

[edit] I changed the settings for attacking fighters and non-combat ships to point blank in the combat strategies... but won't be able to test the improvements until I finish some planet texturing (hopefully) this week.

You can edit individual components of each strategy as well. So eg change the Point Blank strategy to engage planets at maximum range.

The items you were complaining about are under your control, yes. Do you have total universal control of every possible sort? Of course not. However the complaints you made suggested there were aspects you may not be aware of, because many of us have experienced them and addressed those same issues. The strategy definition tools are not all that straight forward in some ways, but they do provide options.

You can't change strategies in mid-combat, obviously. But you can define your own custom strats to deal with different scenarios with some flexibility.

For example, set your strategies to have different ranges for different target types if you need to. For example, I sometimes define strategies that have planets, weapon platforms, troops, and facilities set to "Do Not Engage", while ships are still set to engage at some range.

If I'm using a ship/weapon combo that does what you describe (ie chase ships not closing enough to get in range), I'll test it with different engage distances in the simulator. I've learned that going to medium or short range in a strategy definition often makes the difference in an acceptable fashion. I learned that "short" range really isn't all that close to "point blank" like I thought it was.

The issue of figuring out a way to keep ships from overflying a planet in pursuit of fleeing enemy ships is one that is difficult. That can hurt.

As for changing a ship's assigned strategy to be different from the one assigned to that design in the ship menu, you're correct...you need to put it into a fleet/task force and assign the "new" strategy to that task force. Not ideal, but it's always been enough to get me what I need.

What about holding station around a warp point? Is there any way to keep ships from drifting off as a result of combat?

No, unfortunatly not.
MM needs to add a 'save positions' which reset at the begining of your turn.
The drift does allow you to launch several waves in which can disrupt their formations enough to allow you to win though

Lobby MM for the "Drop Space Anchor" option