On a more serious note, the weights added by Trevor Gore, referenced above, are for minimizing energy losses into the sides. They are nothing as crude as ballast. The suggestion of guitar supports is a good one as that would stabilize the instrument. I just don't like the look of them. But if the imbalance needs correction, supports may be the best answer.
Yes, I totally forgot the point I was trying make. If a weight is added permanently to the sides it might have a secondary effect on the sound. Whether that is good or bad needs testing.
It seems to me to be obvious from the OP that the guitar is neck heavy. Unless a support alters the balance point, then using one won't alter that. I don't see a problem with adding weight to the other end, especially as it could be trialled without damage. I don't have many guitars, but none of them are out of balance in that way, they all rest on my thigh without any strain on the left hand.
"When I was younger, I could remember almost everything, whether it happened or not." Mark Twain