Um, DarkSkies.....I wouldn't advise the use of sulfuric acid.....first off, it is very, very nasty stuff....I worked with it routinely years ago (I even designed and built a wastewater treatment system to deal with the effluent from the process we used it in).....and you have also given some wrong information....sulfuric acid WON'T melt PVC......believe me, I know.....we ran it thru PVC all the time in the process I designed........but it will eat thru copper and other metal in very short order. And it also won't dissolve soap, as soap is a lipid (fat), and fats are generally not soluable in acid (that's why oil and vinegar don't mix......
And if you employ a septic system as opposed to city sewers, sulfuric will kill all the bacteria in the septic tank, causing you bigger problems that the clogged drain.
If you get to the point that you need a strong drain cleaner, you need to use sodium hyroxide (NaOH) pellets mixed with water. With hydroxide, you also need to be careful, because it is quite caustic. And when you mix the pellets with water to dissolve them, the mixture will get very hot from the reaction/heat of dissolution. It will burn your skin (chemically) in short order.....if you should get skin contact, you need to immediatley flush with water until the skin doesn't feel "soapy" anymore, which can take a long time.
But sodium hydroxide will dissolve soap and hair build up in short order, and while it CAN eat the pipes if left in them for extended periods, it takes much longer to do so than acids, and you can flush with plenty of water to prevent that after the clog is dissolved. And while still not great for a septic system, it is not as bad as stong acids, and small amounts can be digested by the bacteria.
One last word.....the air or water pressure things are okay in some instances, but you need to make sure you are using them where the system is "closed"....most bathroom sinks have a vent in the bowl for overflow protection, so if the clog is past the vent and you use pressure in the sink drain, the pressure is just released thru the vent, and won't build enough to clear the clog. The same holds true if the clog should be after the roof vent pipe.....all that pressure applied will just fly up the stack.
Just for future reference, as it seems Paul's problem is solved for now....