OK. 7V rules out the 1646 since the minimum is 8V.The nominal supply voltage is 27.5V, but it has to operate down to 17V.
To minimize power dissipation (so it will work at higher temperatures), I am trying to keep the supply at 7 volts.
If the elevated temperature requirement didn't prevent it you could use the 1646 on 28V single-supply by using the differential output to directly drive the transformer primary and connecting a capacitively-bypassed rail splitter to pin 3. That biases the outputs to mid-supply producing an intentional 14V CM (not differential) offset floating both ends of the primary. See: viewtopic.php?f=6&t=261
You can also parallel multiple 1646s to split the dissipation since they have internal 25R ballasting resistors. The 1646 is also available on a SO-16W package with 80 deg C/W junction to ambient. It's the better package of the three for high temp. Still you may not be able to meet your elevated temp requirements though. It's not a world I often have to design for.