Hey, not on the rug!
First, I have to point out that I consider myself very much a "re-learning archer". I quit bowhunting (and bow shooting) to rifle hunt with family members. Getting back into it now, and am mostly having struggles with form consistency. Point being, my advice may not be the best you can get here. I still hope I can help a little, and encourage some also......
So...I decided for the past few days to just shoot without thinking. I have been shooting at 10, 15 and 20 yards. I pick my spot, go through my sequence and let the arrow fly. Miraculously, the arrows seems to be going roughly where I want them to go. I'm noticing more issues with left to right variation than I am with up and down. And I'm noticing those issues as I get more tired.
This really hits home to me. I pretty much have the same thing going on. Now, I love to shoot groups, or at least attempt to.
On the shot right-to-left variation, I've done 3 things that have helped my shooting, personally.
1. Focus on consistency of
ALL PARTS of my shot cycle. Get this fundamental down to the point where you're almost bored with it. I will practice simply swinging my bow arm up with my elbow in my shooting position, without even pulling back on the string. Next, I'll introduce pulling to anchor, but not shooting the arrow. And so on, through the little individual details of my shot cycle.
2. A clicker has helped my draw and release be a bit more consistent. As per the above advice to focus on all parts of the shot cycle, it's helped me focus on pulling straight back with my release, using back tension.
3. Like you, I found with my 59# recurve, my groups went to crap as I got tired. I went down to my 50# longbow, and it was pretty much more of the same. Somewhere here in this forum, I found the advice to just shoot 1 single arrow at a time. It makes me focus on making the most of this one shot. I try to visualize each shot as a shot on a deer, and I HAVE TO make it count! Kinda pretty much like in a hunting situation, which, like you, is my ultimate goal. One arrow at a time gives me way less fatigue, a better "mental outlook", because most of my shots hit closer to where I want them to hit, and I get a bit more exercise with all the walking.....
At any rate, I hope this advice is good, and that it helps. That's my intent here. If it's not, I hope someone with "better credentials" will correct me.