You don't need an output transformer with a gapped core, because you do not need to put any DC through the transformer. This is just as true for the 2520 as it is with your Melcor. Gapped cores are for single-ended circuits that intentionally put the output transistor's DC current through the transformer primary, such as the Neve BA283AV. In theory there shouldn't be any DC on the output of the Melcor OR the 2520, but in practice there is a little bit - a few millivolts, maybe a few dozen. But you don't need to send that through the output transformer. If there's a lot of offset on the output of the amp you're using, then use an output coupling capacitor. Yes, I know there's no coupling cap in your original API 312 schematic. But there's no Melcor 1731 either. Slapping a cap in there is not a big deal.
If the offset is low, you probably don't need the coupling capacitor. As you can see in the schematic, the 312 had DC coupling to the transformer and it works fine, even though the 2520 is not a precision amplifier (meaning it does tend to have some offset).
I'm being kind of vague because I don't know exactly what the limit is in terms of how much offset you can have and still get away without a coupling cap. I converted a bunch of 325 cards into 312 circuits a while back, and I burned out a pair of 2520s while running them DC coupled to the output transformer. I was also running them on 20V rails, and I don't know which, if either, of these factors caused the amps to burn out. But that's one possibility for you. The other is that the modest DC bias on the transformer will reduce low-frequency headroom, causing an increase in distortion. This DC can also magnetize the transformer, causing a semi-permanent increase in distortion. Who knows, this could be why people like the sound of the API 312. 2nd-order distortion is known to be pleasing.
If you do decide to use a coupling capacitor, it should be a very good cap (Panasonic FM would be my choice), it should be large (2200 to 4700 uF), and should have the lowest voltage rating available - probably 6.3V. You might as well measure the offset and install the capacitor with the correct polarity, although a reverse-bias of less than a couple hundred millivolts is not going to ruin the capacitor. There is the theoretical distortion caused by the reverse-bias that occurs on the negative half of the waveform, and if you're worried about that then buy a bipolar capacitor instead. It also wouldn't hurt to bypass the electrolytic cap with a small (.01 or 0.1 uF) film capacitor - a nice polypropylene cap would be good here.