To be totally honest with you once someone uses any chemicals in a drain / sewer I charge an extra $100 as I already had one employee lose an eye in 1989 as he was splashed with chemicals that contained lye.
First off many (chemicals) if not all are totally useless as you found out for drain cleaning.
Secondly they can be dangerous to people working on the lines and last they can ruin a snake wire.
A kitchen sink stoppage, I find a snake is useless for a decent clearing of the lines.
Picture yourself with a cup of grease place your finger in the cup pull it out and see the grease close up a few minutes after you take your finger out SAME principle using a snake.
Now if one would take a water Jetter and use a 1/8" hose with even as little 1,250 PSI the spray nozzles would scour the lines and restore them to a like new full flow condition without the dangers associated with chemical treatments.
Whoever said you can not snake or water jet a waste line with a garbage disposal had better come to NYC and help me remove several million disposals that other plumbers had no idea can't be snaked as many of us clean the lines in spite of being told it cant be done .
I guess if one listens to an aeronautical engineer a bumble bee cannot fly as the wings are way to small to carry the massive body weigt to wing ratio.
Same with the garbage disposal theory about it can't be snaked or water jetted
In other words every single home all across America with a disposal that has a stoppage has to remain blocked up as the disposal wont allow routine cleaning.
I think you should contact a professional licensed plumber and have her or him clear the drain with the disposal in place watch how they do it so you too can become an expert at doing the impossible.
Have a great week end