Even when not short drawing (for the first few shots) I notice I can't pull my elbow all the way back as much as with the lighter bow - will that always be the case whenever ones goes lighter?
You should be able to draw any bow you shoot to full draw, which is where your forearm is alligned with the arrow, viewed from above. When you draw heavier bows, your body may become compressed so your draw length is not as long as it is when you are drawing a lighter bow, even though you are still coming to full draw.
If I couldn't draw a bow to full draw, I wouldn't shoot that bow. I recognize your problem, in that you want to be able to draw at least a 35# bow, which is toward the minimum end of bow weights as far as being able to get any kind of performance out of it. You made reference to some shoulder injuries, and I guess the most important thing is to get those taken care of first. A physical therapist could advise you best, but I would assume you would be told to not push it and just draw whatever weight of bow you can draw comfortably until things are completely healed.
I'm shooting a left-handed bow on alternate days as part of rehab for tennis elbow. It really does seem to help it to pull one day and push the next with ultra-lightweight bows. So I can sympathize, as I have a wall full of heavier bows I would like to be shooting, but it is more fun to shoot the lighter bows than not be shooting at all.