[Arran]

The end of the cable on that Philco looks like a tube base, unless it has more fat pins then usual. It also looks like it has seven pins, so basically the same base as a 6A7 tube, so an old style seven pin socket may work in the battery eliminator. One plan I saw for a battery eliminator was in an old magazine I have, they used the same trick they used in early AC radios by tapping into the negative leg of the B supply with a voltage divider resistor, basically the divider was between the B- point and the center tap of the high voltage winding of the power transformer. It's not actually a negative voltage as such, but that the B- is more positive, so it works out about the same. The more modern way would be to use a lower voltage transformer, and reverse bias the rectifier diodes. It isn't that it's that complicated to make with all new parts, but I think it's more fun to make ones out of salvaged parts if you can get away with it.
67.5 volts is 1/2 of 135 volts, but 135 volts is also 3 X 45 volts, so many sets used the configuration of 45, 90, and 135 volts as well, and if you look at the tube manuals many of the power output stages also have a 180 volt rating, which is 4 X 45 volts, and some higher end battery sets did do this, at least in Canada. I have no idea if any in the U.S did this, I haven't really perused through the Riders to find out, though Sears or Montgomery Ward may have. I think the logic may have been to just offer a 6 volt vibrator model to those whom wanted a higher performance farm set. Unlike solid state equipment I think that the B+ voltages in farm sets may have had more to do with configuring, and packaging multiples of 1.5 volt cells in series then critical operating voltages. Obviously you would not want to exceed the recommended filament voltages, but running the B+ a little high would no blow anything up, in three way portables the B+ was often as high as 100 volts in AC mode.
Regards
Arran