I don't know what your resources are, but wound packing is supposed to gradually reduce the wound size, as it gradually granulates in, not get larger. On the other hand, half a golf ball is not very big (at least to the eyes of a surgical nurse: me), even though it seems like a cavern to you.
The main thing to know is how does the tissue look in there? is it reddish pink, or is there weird drainage, sloughing tissue, etc. to indicate there is an ongoing infection or other wound healing problem? Another thing I find odd is that you are having wound packing done three times a week. Usually, you do not leave packing in for days at a time. It generally is changed daily or more often. Plus, this is something you could do yourself, unless it is in an area you cannot see or manage. Still, someone in your household could be trained to do this. Seems like a real hassle to go to the doctor so often for this.
That aside, if there is no forward progress after a week or two, the surgeon should be involved, or you should be referred to a wound specialist, often this is a specially trained nurse. Other healing methods can be used, such as a wound-vac, or antibiotics, if needed. What concerns me is that your GP is not contacting your surgeon. You'd think that would be a faster pipeline to his ear...
I had a wound infection that split open my wound, festered, got worse, and required packing too. But, once opened, cleaned, and packed, it was OK.
Jan