Could you not use the 2503 as 1:1 / 300Ohm:300Ohm on the output? That way, you'd get the "authentic sound of API". or any 600:600 on in or out?
FWIW, - Why do you need to transformer-link it to the outside world? I have many pieces of gear that are not balanced, and work totally happily with each other and with balanced stuff. Noise never seems to be an issue, and I prefer my Helioses, for instance, "as is", un-coloured with any transformers on the output, and on the line ins. You could save a lot of money by NOT adding trannies in my book. Of coarse, you might be wanting "That" sound . . .
Good Luck!
ANdyP