SOLVED
Good morning,
I have another update after the second tech visit (I was surprised to see him here 10 minutes earlier than scheduled 
).
1) Different tech
2) He said the terminated splitter needed to stay on because there was nothing in between the modem and the line to the house to bring down the signal. It's simply just too high.
3) The news he shared to me about the possibility of RF ingress said that "It could happen, but highly unlikely." The reason the modem chose other channels, and not the ones that match up with over-the-air channel frequencies is because it looks for, in layman's terms "the shortest line with least number of people".
4) However, when checking the signal from the line at the pole tap, what he did find were several of hundreds of errors on all of the frequencies which meant the guys in bucket trucks needed to look at the (I forget what abbreviation he used; AEC? AGC? AEG?) - basically, the box on another pole near my house. He said the very cold temperatures could indeed have a factor in the mess.
These hundreds/thousands of errors, he confirmed, is what was causing the numerous T3 timeouts, and the eventual T4 timeout if it happens enough.
So, basically put, it's something on the line before my house after all, not the modem. He noted that the reason why the other tech said I might have a bad modem was because he didn't check the line for errors, which makes sense, because without doing so, there's no way to know the real cause.
Different tech said he'd put it in a maintenance ticket today and the bucket truck guys would be out here today at earliest.
As for the SNR, he said 32-33 is still "ok", as long as it doesn't hit 30 (which it hasn't) then it should not cause any problems. The thousands of errors on the line is the main culprit behind the spotty connection.
I probably left some details out due to lack of sleep from last night, but overall, from what he explained, it gave me a clear view of the real problem. He knew what he was looking at and checked everything this time, so I'm confident the real problem will be addressed now.
Edit: Updated signals. My modem chose channels 3 and 5 with no problem. I also have all of my Upstream channels back.
| Channel ID | 4 | 3 | 5 | 6 | |
| Frequency | 525000000 Hz | 519000000 Hz | 531000000 Hz | 537000000 Hz | |
| Signal to Noise Ratio | 33 dB | 33 dB | 33 dB | 33 dB | |
| Downstream Modulation | QAM256 | QAM256 | QAM256 | QAM256 | |
Power Level
| 7 dBmV | 7 dBmV | 7 dBmV | 7 dBmV |
| Channel ID | 2 | 1 | 3 | 4 |
| Frequency | 24200000 Hz | 19400000 Hz | 30600000 Hz | 37000000 Hz |
| Ranging Service ID | 13312 | 13312 | 13312 | 13312 |
| Symbol Rate | 5.120 Msym/sec | 2.560 Msym/sec | 5.120 Msym/sec | 2.560 Msym/sec |
| Power Level | 45 dBmV | 46 dBmV | 45 dBmV | 45 dBmV |
| Upstream Modulation | [3] QPSK [3] 64QAM | [3] QPSK [2] 16QAM | [3] QPSK [3] 64QAM | [3] QPSK [2] 16QAM |
| Ranging Status | Success | Success | Success | Success |
| Channel ID | 4 | 3 | 5 | 6 |
| Total Unerrored Codewords | 111737118 | 110181589 | 110186988 | 110115754 |
| Total Correctable Codewords | 627521 | 639896 | 633666 | 706818 |
| Total Uncorrectable Codewords | 11380 | 10353 | 11321 | 13519 |
