I had this exact same problem on a '98 Dodge 1500, and I changed every sensor (except for two), did all the things you have done, and even rebuilt the engine (twice) before a dealer finally told me the problem... crankshaft position sensor. I had changed every sensor except for the camshaft position sensor and the crankshaft position sensor, because they were the most expensive ($150 for camshaft, $300 for crankshaft) and were dealer only parts. I also thought, either they work, or they don't, no in-between.
I don't know if your '93 Explorer has either of these sensors (I believe it has both)... if it does, that may be your problem. My cats did exactly what yours are doing, and had them checked (perfect). Check engine light never came on. The truck would idle fine, but would cut out when accelerating, and be fine once I got up to speed, with a miss every now and then. It finally got so bad accelerating that I couldn't get above 15 mph and it started overheating (hence the rebuild). After the rebuild (and new radiator), the truck was still running the same and still overheating, the reason for the second rebuild, thinking I messed something up since the first rebuild took me a day-in-a-half. I didn't.
The situation you are describing is exactly how mine started off. If you have a crankshaft position sensor, I would try that, even though it will be expensive. I had called every Dodge dealer in town (about 7) when the last guy finally told me, normally the crankshaft postition sensor goes completely out, but every now and then it will work intermitently, and will cause the vehicle to "stutter", and the check engine light will never come on because the sensor is still technically working.
Changed the crankshaft position sensor, and the truck ran like it was suppose to (I changed the camshaft position sensor afterwards as well since it was the only old one left). I drove it for 3000 miles to make sure there were no problems, I then sold it to a company I deal with, and bought a Ranger. The Dodge is still going strong, 3 years and 60,000 miles later.