I admit I haven't done any calculations, but it does surprise me you found more losses in the primary, than secondary windings. I would have thought the copper losses in both the primary and secondary would be similar and the resistance of the secondary is only lower, because the current rating is higher. If what you say is is correct: the secondary has negligible copper loss, then you should be able to increase the current rating more, not less, with a biphase rectifier, as it only increases the losses in the secondary.
Wait, I might did it wrong. So, here is the tranny I have:
230V primary (14.5Ohm), 2x15V secondary (0.3Ohm each measured with two-wire method, so not completely reliable data), 120VA. Seems that full power and on each winding the power dissipation is I^2*R and:
(120/230)^2*14.5 = 3.9W on primary
(120/15/2)^2*0.3 = 6.06W secondary (each).
Measuring secondary resistance reliably is hard with tools I have

. But even in the best-case scenario losses are comparable. So, I was wrong (at least for the tranny I have).