Cam position synchronizer alignment accuracy required

I’m going to replace the CPS and synchronizer in my F150 2000 4.2l. I have the plastic alignment tool, but I was testing it, and it has a small amount of play in the alignment. How critical is the position? If it’s off by say 1/2 °, can the PCM compensate for that, or does it not matter?

Reading up about it, shade tree mechanics say “the tool is a waste of time”. The Camshaft Position Synchronizer | The Ranger Station

Apparently, it will either be off by a whole bunch (way more than 0.5 degrees) or dead on.

As for the consequences if you get this wrong - this engine isn’t interference (I checked), and if the timing is way off, it’s obviously going to run roughly and have trouble idling, but it probably won’t destroy the engine, you’ll have a chance to correct the mistake.

Yes, I read about how to set the position without the tool (by marking the CPS “flag” position and the housing position with a sharpie). But, even that method can result in some slop, since even if the flag position is dead-on, the housing is not keyed, and can be off by a degree or so.

I’ve tried to find some information about the PCM (or ECM as it’s also called), to see if it is adaptive - if it advances and retards the fuel injection based on measured engine performance, and not just the signals coming from the CPS. I haven’t been able to find anything about that, though. I suspect it’s not a big deal, or people would post about it. As far as I can tell, the CPS is only used to time the fuel injectors - the spark timing is derived from the crank-angle sensor (which seems a bit redundant and backwards to me, but there must be a historical reason for it).