Mine did this before I bought it. The lady that had it from new brought it into the dealer where I was working, saying it was doing the same thing. One of the techs worked on it, had me order a coil from a local parts store. Still to this day don't know what he did, but it hasn't shut down on me.
Could definitely be the coil flaking out when it gets warm. I keep forgetting this is a distributor car....I have had intermittent ignition problems on my COP cars, but obviously only affecting one cylinder at a time. When one of mine starts to die, it begins happening only when the car is warm, and eventually gets worse and worse and happens more often.
Since my driven cars are COP, it only affects one cylinder at a time.
Since yours is distributor ignition, you have ONE coil for all 6 cylinders, and electricity is distributed through them from the rotor to the cap to the wires to the plugs. So a flaky coil is going to kill all 6 cylinders. Didn't notice you hadn't replaced it yet.
After re-reading this, your problem is sounding more and more like a flaky coil or associated wiring.
Whenever I have a clogged catalytic on something, the car feels down on power, especially under load. It also usually smells hot.
The muffler isn't important. Sounds better without them. The flanges between the y-pipe and mufflers always rust out. Every original exhaust I have seen on these things is either leaking or broken here. I just chopped both mufflers off and ran a single pipe straight out the back on mine. But I'm not really one for aesthetics. You could just cut out the flanges and weld in a sleeve. Exhaust shop wouldn't charge more than $100 (probably less) for this. But it's the least of your problems until it stops shutting off.