If you think that it takes more than rounded shoulders to cause this problem, I don't think you understand just how bad the rounded shoulder problem is. Practically every muscle in the upper body can have a non-optimal length-tension relationship.
Start by spending 20 minutes in the position shown in the pic I will try to attach. Note the rotation of the arm and the hand/thumb position. Part of the time, try to actively stretch the hands away from the shoulder. Obviously, you don't need the blocks shown in the picture; a pillow works fine.
Keep spending time in the position. You'll find benefit to just 5 minutes. And you can increase the height of the pillow your elbows rest on, in order to increase the stretch of the muscles around the shoulder.
(Attribution: the pic comes from Pete Egoscue's book Pain Free. IMO this is absolutely the best way to decompress the spinal discs and get them all in their best position, and it is amazing how many problems then get better. You'll get some thoracic extension while reducing tension from the internal rotators, pecs, and lats, as well as all the other muscles down the arm.)