I would NOT pour anything down the drain that generates gas
because you might develope enough pressure to crack the
plumbing if things go wrong.

I don't own a shop vac either, but I use one every now and
then that I borrow from friends. Surely you know somebody
that you can borrow a shop vac from for an afternoon.

A shop vac could be used as a suction device to pull the
blockage back up the way it went in. After closing off
the vent pipe on the roof, you might be able to use the shop
vac to blow into the other operating drain that you
mentioned and dislodge the blockage that way.

In any case, a shop vac is not going to produce pressures
that can crack the plumbing.



Interesting you should suggest that. I don't have a shop vac...but it
occured to me that a solution of vinegar and baking soda down the drain
might blow whatever is blocking it loose if I also plug the sink. It
produces enough effervescence to blow out a hose connection on a boat if
you're not careful. I don't THINK there's any danger of that happening
in the house, but I'm not sure what else might!