Plumber arrived yesterday afternoon. He first tried to auger the toilet. Toilet still bubbled up when flushed. He determined, since everything ELSE in the house was draining fine, and there wasn't a blockage in the toilet, that the toilet must have a crack somewhere inside, which was causing air to leak in, thus causing the bubbling and weak flush.
He said the toilet might still work for a while, but if it suddenly failed completely, it would no longer flush at ALL. Mom and I consulted with each other, and decided, if it eventually failed, it would be a "messy" situation, especially if we couldn't get a plumber here in a timely matter.
So, we went ahead and let him replace the toilet. After he removed the old one, he noticed the house had settled a bit, so, in order for the new toilet to set firmly on the floor, he had to replace the flange, which involved using a blow torch.
After he was finished, we were out $699 total for parts and labor. HOPEFULLY this will be the LAST we need to do for the bathroom for a while! We had the bath tub replaced a few months ago, because the old one was rusting in spots, and had new fittings put on the sink a few weeks ago... so basically, we have an all-new bathroom!