It's quite understandable why Coilcraft won't specify a higher dielectric strength of the transformer than needed in the dedicated application, even it can be possibly achieved.
So the first step would be to check with a test voltage appropriate for 700V operation voltage. As said, partial discharge free operation is essential for long term reliability, it can be easily determined for interwinding insulation, but not so easy for intra-winding.
I imagine, that class 1 enamelled wire (1UEW) or similar material must be used to guarantee the higher dielectric strength. Unfortunately, the copper fill factor is considerably lower and also the minimal conductor diameter is restricted.