Okay, I'm thoroughly confused now with the additional troubleshooting I've done today. I'll try to summarize today's findings below and add a couple of pics. Also note that I still have not received a response from my dealer in over 2 weeks - I don't think they're doing tire rolls right now, so it's possible there's not much they can tell me anyway.
1. Like I mentioned, a laptop plugged into the camera end of the CAT5 in question outside was able to connect to the internet with a fast, stable connection
2. Camera plugged directly into the POE switch using the same port that is currently being used DOES NOT work
3. Camera plugged directly into any other open port on the POE switch DOES work (is getting power and a live camera feed in my C4 app)
4. Plugging the camera into the CAT5 in question back outside and then plugging the switch end of the CAT5 in question into any other open port DOES NOT work (ie, the camera doesn't get power or a live camera feed)
5. Using the tester again as suggested above, but just reversing which end went where yielded the following results:
Outside - the rectangular 'box' like tester scrolled through all 8 LEDs, but #8 was dim
Inside - the 'pen'-shaped tester lit up 1, 2, 5, 6, 7 and 8 with 8 again being dim. 3 and 4 didn't light up