I have access to a treadmill, and living in the Northeast during the winter time I generally prefer to run indoors from December through about March. I do occasional long runs, but the goal of my weekday treadmill runs is to keep up my conditioning and perhaps work on some speed.
Not a scientific answer, but one from a lot of experience…
Don’t run faster during your jog periods. If you don’t recover during these times, you won’t perform optimally during your intervals.
Addressing the safety part: only change one aspect each workout. So in your next run you might try running at a faster pace, but keep the durations constant. Then next week, keep your pace at its new, faster rate, and bump up the durations a bit. But running faster for a longer time is an invitation to injury.