Are any of your P-traps detachable (ie either a cleanout or removable at the elbow)? Would give you a good point of access for a snake.
I would agree on NOT pouring liquid plumber/Drano down. Success chances are low with that much of a run, and then as you mentioned, you're now dealing with very caustic chemicals when you go to unplug downline after it fails.
Do you have any other sinks downline from there? I had a similar situation and ended up busting out the clog from a cleanout in the lower level by sending the snake upwards. Again, very very glad I didn't have Drano shooting out at me (the sewer goop was enough thanks)
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