You don't have to remove the rocker arms to replace the push rods. You can replace by just removing the tension on the rocker arms, as I recall, and install them from the top. But, if you are replacing the valve seals and springs, rocker arms must come off. I wouldn't mess with the head unless you are having other issues, like cooling or compression loss.
Don't know what you mean by lifting device. I just picked the motor up and set it in place with my arms. I put it in a wheel barrow to move it from tractor to shop table. Not that heavy. I'd guess 100 lbs or so.
As far as parts, I would definitely go to a full service JD dealer to get them in person. Tell them what you are doing and they'll make sure you get all the right parts. I would not buy parts any other way.