I presume that you made typo mistake when you said that the right elbow must be in a push position (rather than a punch position) because a push action (10-3-C) is not used in a full hitting stroke.
Oops, you are right, I corrected it!
Comming back to 4 barrel: have you tried it?
Do you feel it difficult to do?
If the gain was so little as stated by Homer why Ted (the Hitter's poster's boy) would be using it instead of 3 barrel?
My intuition is that maybe it is easier to do as it seems and maybe the rewards are greater than Homer thought?