309 should hold this stuff together. You could also use a 409 or 409Cb. There may be some differences in corrosion resistance, so if the part to be welded is in an aggressive corrosive environment, this issue would require more consideration. 420 is a very hardenable martensitic type of stainless steel and should be avoided whenever possible.
The material that you are joining is an aluminum stabilized ferritic type of stainless steel based on looking at the chemistry. This is a weird composition. I have never heard of type 406, nor is it in any of the standards that I looked in.
Are the P & S values you listed maximums? If the P & S contents are high you may see some cracking problems.
Regards.