If the 1345 code has nothing to do with the timing then why does almost every search about it on the web say that it is almost always the cam retard being off which is corrected by adjusting the distributor? I cannot get the readings obviously to see but, just the slightest movement of the distributor can throw it out of wack.
The ignition timing is controlled by the crank sensor and the reluctor on the crankshaft. The distributor has NOTHING to do with the
timing. You are aligning the crank sensor to the cam sensor.
The position of the distributor affects how the spark jumps from the rotor tip to the spark plug terminal of the distributor cap. If the distributor is out-of-position, the spark can fire to the wrong terminal. This is particularly a problem when a spark intended for Cylinder 5 fires Cylinder 7 instead. 7 has fuel and air, but little compression so it ignites easily--and blows the crankshaft the opposite direction.
Wild guess with no evidence: Find a clamp-on high-voltage probe for ignition systems, connect to coil wire. Run engine at ~1100 rpm. Turn distributor to position of lowest indicated voltage. This coincides with cam-to-crank alignment.
"I" just use a real scan tool and do it based on the service manual procedure.
Have you considered that there could be twenty other things that cause the engine to run bad, and the P1345 code is just a coincidence? (Yes, it would still need to be corrected. If that doesn't entirely fix the driveability issue, you'll also have to deal with whatever is REALLY causing the engine to run bad.)
My '97 7.4L was 29 degrees out-ot-alignment when I bought the truck, and didn't run a bit different when I got it within one degree. It did keep it from resetting the P1345 code again, though.