Wow! The mystery that won't allow itself to be solved! Where's Agatha Christie when you need her??? Well, now it's time to reach for the oddball causes beyond the usual suspects that you have eliminated. ALL of the following have happened to me, usually at the worst possible time in traffic or out in the desert on cross-country trips and caused some or all of the symptoms you are experiencing.
Carburetor - Sometimes the little nub on the choke arm comes out of the choke driver's groove, allowing the butterfly plate to float freely inside the intake mouth. You can't really see that unless you are specifically looking for it. The carb will not choke because the plate doesn't respond to pulling on the choke rod. The engine may be hard to start unless you are one of the lucky ones, whose Model A starts quickly in and out of season. It's when you are driving that problems arise. That plate can vibrate closed for a couple of seconds, which will make the engine run rich and even stop it. The carb is literally choking itself with that plate in the closed position. You write that you have changed carbs. Two carbs may have the same short choke arm nub. Manually inspect the choke arm to see whether the arm is loose and that the choke plate moves with the arm.
Battery - Many guys don't bother putting a holddown frame over the battery to keep it in place, either because they don't know there is supposed to be a holddown frame over the battery, the battery is too small for a holddown frame to be installed and/or they are too cheap to buy one. If the battery is free to move around, the negative terminal's battery cable end can touch the brake pedal's rod, especially when you hit the brakes, make a sharp left turn or go up or down a steep hill. This shorts out the ignition until the battery moves away from the brake rod. When your engine misfired and then cut out completely, the battery may have moved away from the brake rod when you pulled over to the side of the road. Make sure there is a battery holddown frame over the battery and that it is tightened securely.
Distributor - Just to save 1/1000th of a penny per distributor per car (times 5,000,000), Henry used the bare minimum length for the wire that connects the lower plate to the ignition points on the upper plate. And that wire was WAY thicker and stiffer than it needed to be, which has caused owners headaches ever since. That wire becomes brittle with use and can break or work itself loose from the ignition points, causing misfiring and stoppage. Check the wire's condition for fraying and looseness. Better yet, replace it with a longer, modern wire that will allow the upper plate to move more freely.
Also, if you have the so-called "modern" lower plate with the plate that touches the upper plate instead of the wire (or is it visa-versa?), deep six it. I haven't experienced this one, but I have read that this plate doesn't do its job and loses contact with the upper plate = loss of ignition. Go back to the original design with a modern, flexible connecting wire.
Ammeter - Pull the instrument panel forward and inspect the back of the ammeter. Ensure that the two wires are secured tightly to the ammeter and that they aren't burned or frayed. Get your nose into things and smell the wires. That can tell you if they have gotten hot and are possibly burned inside. When lots of juice is flowing through them at higher speeds, burned or broken wire strands inside the cloth covering will allow a breakdown in electrical flow. That you experience problems above 40mph makes this a strong possibility. Replace the terminal box-to-instrument panel wiring harness anyway. Make sure the two terminal studs are not loose and cannot be wobbled. Repo ammeters are notorious for all these problems. If in doubt, temporarily wire a known good ammeter in the electrical system and see if that helps. Make sure the nuts are tight on the terminal box and no wire end flag is touching the metal ignition cable conduit.
Terminal box - This happened to me in 1974 on the Autobahn in Germany during a three-day rain-soaked drive in my 1928 Roadster from Hamburg to Munich. I have written this up before, so I'll just give you a thumbnail description. The 1970's was the nadir of Model A parts quality, mostly coming from off-shore and mostly of poor quality. At speed on the Autobahn, the engine exhibited exactly what the poster says his engine is doing: after a while of driving, the engine began to misfire and eventually shut itself off. This was in cold, rainy weather. The brand-new terminal box I had installed before shipping the car from New York City to Germany was one of those off-shore pieces of garbage that looked nice and shiny, but - the maker had used round head bolts as the terminal poles and didn't sink them deeply enough into the plastic terminal box body. The heads were too big. Just enough of the heads stuck out past the terminal box so that when the firewall got hot and expanded due to the heat, an arc of electricity jumped between the firewall and those bolt heads to cause a misfire and engine stoppage. Drove me nuts in the rain trying to figure out what was going on. After I had pulled over for a while and the firewall cooled back down and contracted away from the bolt heads, the engine ran fine for a while until the cycle repeated itself. After checking EVERYTHING else, I finally pulled the terminal box forward (no easy chore in the rain) and noticed a black splotch on the firewall where a spark had been arcing. It was then that I also noticed the rounded bolt heads sticking slightly past the terminal box body. The heads were too big to be drawn in tighter, so I reached for the spare terminal box I had brought along, whose terminal bolts were sunk properly into the terminal box body. That solved the problem and I had no more misfires during the year I spent with the car in Germany. Pull your terminal box forward and look for signs of electrical arcing on the firewall and inspect whether the terminal bolt heads are inside the plastic. Put a little RTV or hardening gasket goop over the bolt heads anyway.
ADDED: This was not an isolated experience, by the way. In the last 45 years, I have discovered this same situation in three friends' Model A's, all of which had been built in the 1970's-early 1980's with that same &^$#*( terminal box. If the poster's car was built from parts purchased during this time from Rick's, J.C. Whitney or Warschawsky (same owner as J.C. Whitney), he may have one of these defective terminal boxes, whose terminal studs have worked their way back towards the firewall and are arcing.
Distributor body - Some off-shore plastic distributor bodies made in the 1980's were prone to internal cracking, which killed spark to the plugs. A brand-new shiny distributor cap did this to me in the rain on a cross-country drive. For two days in a motel parking lot, I couldn't get the engine to start. I procured locally a used, gundgy-looking original body and replaced the new one. The engine instantly fired up. It turns out, that in damp, rainy weather, the body's internal wires lost contact and wouldn't distribute the juice to the spark plugs. Try a different, know good distributor cap.
Whew! My typing fingers are blistered now! Try these suggestions to oddball causes of misfiring and engine stopping.
Marshall
