Moss, have you ever broken any pipes or caused leakage at fitting joints with your method? That seems to put a lot of pressure on the fittings?
I've never heard of a sink plunger ... just a toilet plunger?
The toilet seems to flush fine, the shower drain is a little slower than it used to be. A sink full of water can take an hour or more to drain. But when I took apart the P-trap I didn't see any restriction including when I examined the pipe after the P-trap.
I've never popped a pipe with a plunger. I don't do snakes. That's up to the plumbers. Although I do occasionally use the 2' long plastic zip strip drain snakes. They'll grab a lot of hair out of the drain plug. Like these:
Did you remove the drain plug in the sink and look down into the sink drain and see light when you had the P-trap off? As other's have mentioned, there can sometimes be a huge blockage of hair and bath products stuck on the lever that lifts the plug.
Also, don't skip trying a chemical drain cleaner. I have two daughters with extremely long, fine, blonde hair. When they were kids, it was down past their knees! So we had quite a few hair clogged drains. The bathtub drain, especially, but the sink drains, too. When they brush their hair, a surprising amount ends up down the sink drains.
I like to use the two-part gel-type liquid drain cleaner. It works most of the time. Liquid Plumr seems to work very well.
But that is only at home. I don't use the chemical at my job. Just remove the sink drain plug, clear any hair and gunk from that, then plunge the sink. 5 minutes and you're on to the next one.
I have a septic system so chemical cleaners cannot be used.
Another person suggested a large quantity of near-boiling water into the sink drain might clear any residual soap clogged into hair along the sides of the pipes. I have never tried that either.
I have a septic system, too. Liquid Plumr says its safe for septic systems. However, I understand your concerns, so try the plunger trick. Can't hurt, and a small sink plunger is only a few bucks. The zip strips are 3 for $2.99.
But be sure and pull that sink stopper out and look down there before doing anything else. It might be just right there, before the P-trap.