I've never had a problem with sleepiness, and I only get impatient when sitting on my own.
But oh that leg pain is something else.
Does anyone have any advice from a Zen perspective - not necessarily how to reduce the pain, but how to not simply hate meditation because of it (at least the half lotus position, and at least when in that position).
As you progress in your sitting and develop samadhi, leg pain will become less of an issue. You will still experience it along with the discomfort, but it stops being such a matter of "oh-my-God-this-is-terrible-ring-the-bell-now" and instead becomes less of an immediate concern. It's almost as if it's happening in the background while your koan or mushin becomes the center of your attention.
Think of leg pain like a tooth ache. When you are sitting around and watching TV with your mind diffused and disordered, you are very much aware of the discomfort. If, however, your mind is absorbed in something else - and I don't know of a single person who'd complain about their molars during sex, for instance - that pain has less command of your attention.
The important take away is to develop your concentration. Follow the breath to its very outer limits. Let your mind ride your exhalation all the way to the end. If you allow your attention to break even for an instant, discomfort, thought, judgement, and opinion will arise in the vacuum.
As a side note, don't sit in half lotus if it causes you pain!!! Use the Burmese posture where you put one foot in front of the other. There is no sense in torturing yourself. If you hate meditation, you won't practice it. Zen isn't about self injury, it's about waking up.
I am a Zen practitioner that lives with chronic pain. I haven't been sitting for super long but I have learned a lot about sitting with pain since I've been in the Zendo.
My first recommendation is that if you have a teacher you ask them what to do.
There seem to be two end of the spectrum on this, and what's important is that you find what the middle between the two is for you (might be different today than it is tomorrow!).
1) As neko elucidated in their answer, the pain is a story. You don't "complain about [your] molars during sex." It can be very important to sit through the pain.
2) If you are causing actual harm to yourself, you are probably doing something wrong. Get up. Go lay down. Change postures. When I'm on retreat it is very important to me that I don't leave the retreat with a destroyed body. I have to balance when I sit with pain and when I stop sitting and take care of myself. I have to be very careful about falling into thought patterns around the idea of zen being some sort of bootcamp.
Think of your leg as already broken and the pain is just a memory.
