Did you check/readjust the new TPS? It shouldn't cause your issue, but it won't help your carb feedback to the ECM if it's too far off.
To me, if it repeats like this, it doesn't sound like a carb problem or a dirty fuel sock. Very unlikely since it seems fairly repeatable.
Although you haven't done much diagnostics at this point, I tend to agree with
MrSony on VERY LIKELY the ignition module. Your 87 307 uses a 7 pin module. And as stated, you need THERMAL paste as a heat sink seal between the distributor housing and the bottom of the ignition module. If some paste is left under the old unit that isn't full of dirt, you can re-use it. It doesn't go bad as it's not like a greased bearing. You don't need much. Make sure if you put new on it, that it's THERMAL paste. It can be dielectric thermal paste, but make sure it's for heat sink application. Or you'll fry the new one, too. If it's dry underneath the module, that's a problem.
Carry a friend and a timing light with you. The timing light means you don't have to disconnect anything to test for spark. As soon as it dies, get to the side of the road if possible, have a friend crank it after you hook up the leads to the timing light, any cylinder will do, doesn't matter which spark plug wire but preferably #1. Have them crank it over ASAP and check for spark by seeing if the timing light will flash when cranking. If none, it's the ignition module AND/OR coil. I've heard of coils conking out after they get warm. Kinda rare, but possible. If you DO have spark, then it may be time to focus on the fuel. If it does crank and fire up, then check the timing mark and see if it's steady or fluttering around. If it flutters badly, it may be a timing chain telling you it may be going bye bye. If it's original, it has nylon gear teeth which are notorious at that age of breaking off and ruining people's fun. If you get it back to the house and it's running, do a timing check on it and make sure it's at 20 degrees with the A&B terminals on the ALDL under the dash jumpered to lock timing while you check it. With the terminals grounded you should see 20 degrees BTDC. And it should be pretty steady.
If you put new plugs in it and set them to proper gap, the 87 307 uses a 0.060" gap. You can use that and shouldn't be a problem, but probably better to again probably reset those to 0.045 to 0.050" max. JMO. It'll run just fine that way and not overtax the ignition system.
Again, try the 7 pin module. Various GM p/ns, but also you can get Standard LX315.
You didn't say WHEN you changed the coil. Was it before the issues or after? As far as any coil change, you HAVE to make sure the polarity is right. Not all HEI coils interchange. Did you just buy a coil from AutoZone or something and let some counter jockey without experience make the call? Depending on what's in the computer, they MIGHT have gave you the wrong coil. Just feeling out possibilities. Still got the receipt or box it came in? Part number? This can help me determine if you got the correct one.
For your 307, 12498336 is the GM part number you seek (or aftermarket equivalent, like Standard DR-32). RED AND WHITE wires. If there's a yellow wire in there, it's the wrong one.
