First off, this is your LJ, right? P0344 is not a possible code listed for the JTEC PCM in your 2003, but it is for the NGC PCM in your LJ, so that's why I'm assuming it's your LJ. Anytime I get P0335, P0339, P0340, or P0344 (which are signal issues with the crankshaft and camshaft position signals) combined with any of the P0300 through P0306 codes, the P0300-P0306 is likely to have been caused by the problem that triggered the P0335-P0344 code, so I'd start my investigation with the P0344 code.
Here's the section on P0344 from the
Powertrain Diagnostic Procedures Manual (I've circled some important things):
View attachment 602928
The top part I circled may explain why "it could seemingly run fine for a few days then have the codes thrown." With an intermittent problem, it could take many trips before you had one where 20 events were observed by the PCM. The Powertrain Diagnostic Procedures Manual is a bit vague in explaining how intermittent codes are handled, so I'm not sure what the process is for the PCM to determine when to light the DTC light.
In the Possible Causes box, there are five I circled that could have something to do with your repair (assuming that you are running that repaired camshaft position sensor). In the sequence of photos you posted, you went from this:
View attachment 602933
To this:
View attachment 602935
You probably didn't, but if you left the red (+5V Supply) and black (GND) conductors exposed and just wrapped the entire assembly in electrical tape, vibration could be allowing the two conductors to touch every so often. When they do, the first "Possible Cause" that I circled (+5V short to GND) will occur.
In your case, I think your plan is solid. Replace that sensor to rule out the shorting. I always recommend rotating the OPDA and performing a Relearn when changing a camshaft position sensor because it's not very difficult, and it rules out that being a cause for code generation. Also, since it was discovered that disconnecting the battery will force the PCM to do the Relearn on the next startup, a bidirectional scanner may not be required. You just need a scanner that can monitor the Cam Crank Difference variable while you rotate the OPDA.
Good Luck!