I think all of pete's advice is good. My additional comments:
I would not use a heat mat, unless room is cold. 65-75 is fine.
I don't think the creepy crawlies you are seeing are the cause of a problem. I think they are a symptom. I think your cuttings had already started to give in to rot, then the creepy crawlies move in. Fungus gnats will feed on living roots, but usually they start off on a dead cutting first, then move to live ones.
I also agree with others' comments that it's likely too much water could be the culprit. It's hard to keep the right balance when winter rooting in the northeast. Indoor air is far too dry, but if you put it in a humidity bin, mold can be a problem due to lack of airflow. So you have to put in a bin and keep it cracked, or you put it in a ziploc and open it every couple days, etc. This way you have enough airflow to prevent stagnation issues, but humidity is still high enough.
After you put a young cutting in a pot, it can be even harder to keep the right moisture balance. The top of the soil can dry out, while the bottom or middle can be soaking wet, and it's hard to judge how much water to add. I have resorted to misting in the past, which works pretty well, because that way there is much less temptation to overwater. I used a 2 gallon mister, which is usually used for pesticide application. But then last year I was too lazy, I just stuck plastic bags over the top of the pots, or put them in large bins.