I have bought an 88 F150 4.9L used. It was having trouble running rich. During troubleshooting I noticed that my firing order is 152634 instead of the 153624. Obviously the 2 and 3 plug wires are reversed. I corrected the firing order and the truck runs very rough as expected with two crossed plug wires. I put them back and the Truck runs fine. I'm not making a mistake, I checked it five times.
How can this be? I know if you change the cam shaft then you can change the firing order. But come on, whose going to throw a cam in an inline 6.
In short - haven't come up with any good ideas here.
Looked at the rotation - even if one went counter-clockwise on the distributor - should end up with the firing order of 1-4-2-6-3-5, so this ain't it.
Don't think it would be the cam - the swapped cylinders are not in phase or sync, so I would think that a cam with that order wouldn't work in this engine. If I did my ciphering right - the 1 and 6, the 5 and 2, and the 3 and 4 pistons should move together.
With the 5.0 - the original firing order was 1-5-4-2-6-3-7-8. The HO version, or for those who stuffed a 5.8 cam in - the firing order became 1-3-7-2-6-5-4-8. The 3 and 5 cylinders, and the 7 and 4 cylinders were swapped in the firing order. This is possible because those respective pistons are in phase or sync with each other, just on opposite parts of the 4-cycle combustion - so a cam change, and related fuel injection harness and plug wire swap are all that is necessary.
When the 3 cylinder is on the compression stroke, the 5 will be on the exhaust stroke. Changing only the cam can reverse this sequence - but only because those respective pistons move together.
For the 300 I6 - changing only the cam would mean that the 1 and the 6, the 5 and the 2, and/or the 3 and the 4 could be swapped in the firing order. To change the firing order beyond this, such as your case of the 2 and 3 cylinders, would involve a crank with a different sequence. Not that this couldn't be done - just haven't heard of any aftermarket stuff that would do this type of thing.
Between this and what you've recently found - may be a case where standard logic does not apply. Again, very much interested to hear what you find out.