Are you proposing applying the H-bridge to one half of the torroid's primary instead of the whole primary? That should double the voltage across the secondary, but be careful if you are drawing any significant power from the secondary, you are doubling the current in the primary. Losses in the primary are proportional to I squared.
The correct way to do this is to rewire the primary as two identical bifalar-wound half-primaries connected in parallel. That would mean separating the two windings at the tap, and reconnecting the four ends of the two half-primaries so as to make only two connections to the h-bridge. The phasing of the two windings is critical...