1939 Apt. Flushometer problem

One of the flushometer (Sloan valve) toilets in our NYC apartment (built 1939) has been malfunctioning lately. The problem starts with the water not remaining at the proper height in the bowl after flushing. If we continue to use the toilet when it is this way, it works fine for 5 to 10 times, then suddenly overflows when flushed. The main super is away for a month and his replacement keeps coming up with a plunger or manual snake and while the bowl will start filling properly after using these for the 8 times he flushes, even with paper, it stops filling up again after about 5 to 10 real uses. This has been going on for 3 weeks.

Once, when we didn't use this particular shower for a while, there was an awful smell in the bathroom and the super told us that we had to run the water in the bathtub regularly because the toilet was connected to or vented out of the bathtub drain. Also, several years ago, the toilet backed up into the bathtub. The reg-super used some sort of high powered jet propelled air gun to clear the obvious blockage. I'm thinking perhaps there is a blockage in the vent, perhaps hair from the shower? Would that cause the water to drain down to a couple of inches in the bowl after flushing?

Now the substitute-super said he might have to take the toilet apart. This toilet bowl is a lovely old one, color coordinated to the original rose and adobe colored tiles and I would not like for the replacement super to break it since I know the landlord would put in a bright white Home Depot tank toilet. (I watched his contractor smash a similar toilet, working perfectly, with a sledge hammer when they renovated a deceased neighbor's apt.) Any ideas for a less destructive solution? Or should I just hope the real super gets back eventually?

It sounds like to me that there's a main line blockage. The toilet will flush fine until the pipe fills up. The more often you can flush before this happens, the further down it is. A toilet auger can only go about 4-5', and won't get to the real problem. Any toilet should be able to be removed without damaging it. Unless there is another cleanout, removing the toilet to auger the drain may be the only choice, but unless the plumber is a total hack, should not damage the toilet or the floor.

The valves can be rebuilt to new condition, too, if that is an issue, but it sounds to me that it isn't.

A good look at the toilet will tell you if it will survive being pulled.
A bunch of small fractures all around the base of the toilet...
Administer last rites.