Goosey
.
Its not just you @steveP lots of people get good carry over from the treadmill to the road. There are even running groups in Melbourne who do 1-2 sessions of their weekly volume on treadmills. I found for me that the treadmill worked well for increasing my running cadence as you have to turn the legs over quick to keep up with the belt. This translated into better running economy and faster times on the road. However for what the OP wants to achieve a simple run 3-4 days a week over the distance required and go harder each time will achieve the desired results.
We got there in the end