There was no blood at his side of the bed - isn´t that a little odd?
There could have been fine spatter that was not described by anyone, they could have missed it or not have seen mentioning it as relvant. There might not have been any spatter based on the exact location of the wounds. As far as dripping blood, it would depend how fast he got up whether he would drip blood. He could have been sitting up in bed, sitting on the floor or in the process of getting up from the floor or bed. Sitting up I suppose is the first step to getting up.
We know he had his left side to the killer and was on the other side of the room based on the distance of some of the shots. (not standing on June's side of the bed with the killer right on top of him) We know he wasn't standing for at least some of them. That's as best as it can tell us. For all we know he fell out of bed when the shooting started because it scared him so much and then was on the floor and getting up as he was shot. We can think up a lot of different reasons to try to account for it but who knows for sure why. We just know in general he was on his side of the bed/room not June,s with his left side facing the doorway and not standing during at least 2 shots. The evidence is not more specific than this.
Further, I cannot quite make your scenario fit with the diagram. The two shots to his left mouth area, OK. PERHAPS the one to his lower left arm, which exited (where did that bullet end up?) ; but not the shot to his left shoulder. How would the shooter have stood near the door achieving that?? It is clearly fired with the rifle pointing downwards in a steep angle.

The diagram is not that good, he draws as poorly as I do. Some of the positions shown are misleading. The bullet in the lower arm was supposed to reflect a graze wound to his elbow! Yeah I know not even close. It grazed off his left elbow and went into his left torso lodging in his torso. That is the bulet that he saw in the xray but was unable to find when he was probing around. He gave up rather than rip his guts apart. So basically he had his arm at his side the bullet grazed his elbow before going into his side. This shot was relatively lateral.
The shoulder wound and the jaw shot were both angled down and high enough on his body that neither alleged shooter would have been able to cause such injury without standing on somethign so he was most likely not standing when these shots were fired.
Because all of these were on his left side it means his left side was facing the killer who was towards the door so his left side was basically towards the door.
The bullet that went through the elbow shattered the Humerus and was found in the fracture.