I would think the surface still needs to be prepped so you might resolve the stain issues before you get to paining with Kilz. We went to a local janitorial supply and bought "J-Works" Degreaser. A product called Virox 5 (Accelerated hydrogen Peroxide) Sanitizer and cleaner) and a liquid enzyme cleaner. Ended up using the degreaser and virox only. The Virox cleaned and disinfected and the degreaser pulled the yellow/brown cigarette residue without issue.
A wise man once told me he wanted to stay fit enough to run a marathon on his hundredth birthday. Another said he wanted to be shot by a jealous husband on his, I'm with the latter. God bless you Richard.
Carpet Cleaning is what I do, it's not who I am.