You could get a roll of emery cloth P400 grit. That is what they use to finish steel ready for chrome plating, which leaves a very smooth surface as chrome plating would otherwise show any imperfections.
2 to 3cm wide strips would be enough to work around those welds as they do to with fillet brazing.
You could even ask at the chromers for some offcuts as they sometimes cut them to size to fit their wide machines and throw away the rest.
There is even like a putty/wax they use which helps during the process.
Very fine '0000' steel wool and Autosol would also help for a better finish but you would have to clean well with soapy water after as the paint might not stick well.