I googled the G and not many pics available of the rear toolbars. I did find one that looked factory. It appears to me to be a piece of square tubing that ran across the back of the tractor, had a flat bar on each side that connected to the tractor to suspend it and raise and lower it, the actual cultivator shank/feet attached to the flat bar. This one had a clamp on factory looking trailer hitch in the middle.
If it was me, I would remove the trailer hitch, weld a piece of 2X2 tubing sticking straight out the back if it was still mounted to the G. This would turn it around backwards from the G application. After mounting my cultivators on the flat bar, sliding out to my liking, I would then cut off all the excess that was used to mount the bar to the G. By turning the whole thing around, you will have to turn the feet around too. If they don't line up right, you can heat and bend the bars to fit, but I suspect they can be loosened and turned, or put the left on the right, right on the left.
If you don't think the toolbar will raise enough coming straight out of the hitch, you may want to bend the tubing up a short distance and then continue straight back before connecting to the toolbar. Measure the height of the lowest point of the tractor and stay no lower than the lowest point, that way you lose nothing with your reciever hitch clearance. Those open middles were for a reason. By bending, you will need to cut it and weld it back together as tubing is not real bendable by the home fabricator.
Are you doing the work yourself or do you have to hire it done?
Someone suggested selling it and buying what you really need. I have a turn plow for a L or LH John Deere as a yard ornament. I have let the local tractor clubs know I have it but seems nobody wants it. They collect the tractors but not the equipment. I have saved a lot of money by reworking a piece to fit my needs, but I do it all myself, not having to hire it out.
If you can post a pic of what you have, I can be more specific on what to do. Or you can send it to me direct.