reverse winding goes way back, farther than Haffler, but if you want to make a living selling boutique audio you have to be a good salesman,
reverse winding will not cancel the dc amp-turns, if it did, then your ac would cancel also. google right or left hand rule.
a magnetic field can only be built one way or the other, the sense of the current relative to the core must be the same to be additive,
you can use non grain lams in .018 gauge to raise your ac and dc saturation levels, and it is cheap.
Partridge made some good output transformers, they knew how to split the primary up, probably came from experimentation,
MacIntosh made some good output transformers with cathode winds and quad filar winds, but that market has changed in a big way,
Fisher made some nice medium range iron, you can get a junker x 100 of evilbay and get the some of the best EL84 transformers ever made, 93 EI lams, (15/16" tongue) why not just skip up to 100 EI which is much more common and probably cheaper? they wanted to get it just right.
Altec Peerless 15036, what a beast! fat stack of 175 EI which is insane for an 80 watt amp, all done with #26 wire, quad wound secondaries, 5 section primary, (wtf?) with a rev wind thrown in plus a cherry on top in the way of 4 lams of nickel alloy in the middle, try buying 175 EI in 80 Ni ! does the Ni do anything special? probably not, these guys were out to showoff to each other because they knew the competition was gonna do a break down on their stuff,
edit: never mind on the X-100, prices have gotten out of hand, this rusty hulk is going for $800, i got one from Kittleson for 150 back in the day, he used to hang out with Eric Barbour on Duane Ave Sunnyvale at the VTV shop, i got to go in that shop and was amazed at the vintage gear that was stacked up, the most impressive was the PA system for a drive in movie , huge chunks of iron needed as car speakers were not out yet, full of giant PCb capacitors, lord have mercy, Fisher iron-best guitar amp you could ever make can be built around these and some Amperex Bugle Boy tubes from the 50's