Low leakage transformers are a challenge.
The decision to make it a pushpull increases the difficulty level. But it can be done.
With pushpull transformers it is very important that each of the two halves in both the primary and secondary are balanced, to minimize staircase saturation.
This means bifilar winding, in addition o interleaving.
In an effort to explain myself better, I've divided the winding segments in colors as shown below.
View attachment 139476
I would wind:
first layer; red and green
second layer: blue and light blue
third layer: pink and lime green.
Of course, you would have to keep tabs on all the wire starts and ends and connect them accordingly.
You don't mention he primary/secondary isolation requirements. You may get away with very thin or no tape insulation.
If the leakage inductance is still outside your requirements, you may need further segmentation and interleaving.
At 1 Mhz, and depending on the calculated wire thickness and the required losses, each individual segment in turn may require to be bifilar. I suspect that the secondary being the higher current one, may require this technique.