In reply to TheFasting:
> So far my main problem is easily identifiable, and it's just that I don't trust any foothold outdoors, so it takes me forever to figure out beta and often I end up just desperately lunging for holds.
You already know what the major problem is, then.
So top-rope sports routes (whether that's by setting up a top-rope or seconding after someone else has led), second trad routes if you can find a partner for trad, and boulder outside (if there's any outdoor bouldering near you and you feel comfortable with that).
Use that to make a conscious effort to learn what footholds you can use, how much weight you can put on them, and how to read the rock in general, when you're in a relatively fear-free situation and can experiment and try different things.
Trying to learn to trust footholds when you're simultaneously trying to manage fear of lead falls may well be too much all at once.
You can't experiment and play with using a foothold to see what it feels like (or see how lightly you can hold on, to avoid over-gripping) if you're clinging on desperately and gripped out of your mind because you're so focused on not falling/failing.
I'd second what a lot of other people have said in different ways --- right now, it sounds like this is miserable and frustrating and a grim chore that you're trying to force yourself to do, when sport climbing is not actually what you find motivating in the first place.
There are some obvious things you can do to make sport climbing more enjoyable and productive, like using it as an opportunity to work on your footwork, which will benefit all of your climbing. Stop focusing on the grades you're leading, put a top-rope on stuff and work on your footwork. You don't have to stop leading, but maybe make leading and fall practice a separate part of your outdoor climbing days.
If sport climbing is a "necessary evil" that you're just doing to improve your trad, then that's an additional reason to treat it as training, not performance (Dave MacLeod's distinction between the two has been super-useful to me).
Take the pressure off, take the fear of failure off, and focus on learning, not performing. Remember that your goal isn't "lead [sport grade X]" anyway.
Right now, it sounds like the immediate goal is "improve your outdoor footwork", and it also sounds like pushing yourself to get on harder sports leads isn't the best way for you to work on that.
And if what actually motivates you is trad/Alpine/mountaineering, then keep your focus on those things. Doing the stuff you actually enjoy and that you're passionate about will make you perform better anyway.
Driving yourself into a downwards spiral of frustration, misery and self-imposed pressure will *definitely* not be good for your climbing.