Can the denture be painted with a gold paint or any other permanent coating to help?
Not as far as I know. I have never heard about it (30 years experience). There is no gold coating. There are dentures made with gold plates instead of acrylic, but I am not sure if that will eliminate your sore spots. You may need to start thinking about a treatment with implants and maybe a fixed prosthesis over the implants. That will eliminate the tissue support of the prosthesis and the sore spots. It will be expensive, but is worth it.