As far as the breeding goes many things can work, cooling not cooling, keeping a hotspot at lower temps at night only, not having a hot spot at all and only use room temp etc, the key is to find what WORK for your animals and for you. I have tried many different things over the years mainly because conditions changed (different snake room and location changing the conditions) and my results were similar. Now I just have my snake room at 75/76 on the winter and a hot spot of 84 (which is about 4 degrees lower than the usual)
Now as far as your actual ambient temps in the 60's if the temp in your tubs is around 60 that it will be unhealthy for your BP, and a combination of improper temps, stress etc will create issues.
You will need to get that ambient temp at least in the 70's and have your rack/enclosure well insulated.