My reply to your problem could be pages long, but I’ll try to do it in a lot less. The pain to your thumb gripping the bow and the cuts are caused by nock placement. Your arrow rests on the bent knuckle of your thumb. Think of a line along bottom of its shaft that is at a right angle to your string. Now go up the string 1 1/2 arrow diameters from that point and that will be a second point which is where the bottom of the arrow’s nock should be on the string. Koreans don’t use nock rings to guide the nocking of an arrow. They may mark the serving or allow the wear on the serving to indicate that nock point. Ring placement to the arrow is about four to five millimeters or a 1/4 inch below the nocked arrow. That’s the top edge of the ring whichever type you have. Koreans have two types. Regardless of which: this spacing does two things. It puts the ring at right angles to the rest. It also leaves a space so that the ring won’t rise up on release and in turn contact and push the arrow up the serving/string. Depending on which type of ring you have, your index finger will be over your thumb for one type or over the horn of the other type. The side of your index finger just past the first kknuckle should be applying a little pressure to the side of the nock and/or arrow shaft depending on which kind of arrow you have. This pressure anchors your arrow and your ring in place. If your serving doesn’t hold the arrow firmly, the arrow may slide forward, so make sure the serving is the right thickness. (An aside: Koreans use two servings, one made with standard serving thread, then one using string material over the first. The first protects the string strands, the second protects the first.) This pressure also helps keep the arrow in the rest’s V, formed by your bow and thumb. This is important as your bow should be canted a little from the vertical. Now I’ve just written a crash course on ring placement which you haven’t asked for. For that, I’m sorry, but you might find it useful.
Now to your anchoring problem. Before I go on, I’ll mention that my draw length is 30 1/4 inches or 77 cm. I draw my arrows until the bottom of the point touches my thumb’s knuckle. That way I always draw the same length. Now to go off on several tangents.
The first thing is: shooting western style and eastern are not the same. I know very little about the former so I’ll just describe how I shoot a traditional Korean bow that some people call a horse bow as it’s a good bow to shoot from a horse. What comes below is not for shooting from a horse. It’s for shooting from a stationary position standing.
Stance: facing 45 degrees to the target, except your head is turned as much as possible to face the target. Head is straight/level and doesn’t move up/down, side to side or left or right.
I’ve seen a number of different arm and bow movements to get to a ready-to-release position. I’ll only mention two things about that. You should be gripping the grip off centre. That is, the larger pad of the thumb should be pressing firmly onto the grip off its vertical centre line at the back. Your wrist should be cocked up and outward. This will help get the bottom of your elbow out of the way of the string on release.
Where you should be once you’ve drawn and are ready to release is this. As mentioned, I draw till the point touches my thumb. This brings my release to around and below my ear, but not touching it. Arm length will cause this to vary. I’ve seen some archers with the upper string past their ear. I do try to get in as close as I can to the side of my neck. What is touching me is the arrow shaft along my cheek and jaw. This will vary with neck length. If the bow were vertical, the upper string might be touching my ear, but the slight cant of the bow takes it away from the side of my face and/or ear. Arrow and release arm should be a straight line. However, having the elbow down causes far fewer problems than if it is up. Release should be fast and crisp trying to get the ring, thumb and index finger clear of the string as fast as possible. You should try to keep your hand motionless except for the fingers.
This is about all I can think of for now so I’ll post it in the hope that it might be of help. Best and many hits.