A word of caution... accidentally setting the volume too high while feeding into the 8 ohm secondary of a 70v transformer, could put 70+ volts on the primary! (Remember: MURPHY!!!) Kiss the inputs of whatever it's connected to "goodbye".
A plain 600 ohm 1:1 transformer will work perfectly.
One thing to be aware of, is if using an 8 ohm step-up to 600 or whatever, you will also be stepping up any amplifier NOISE on the speaker outputs... and you'll need to run the volume control very low to compensate for that step-up, so the noise will be very much an issue. (Don't ask me how I know this.) ;)
If the only transformer you have is an 8 ohm to some higher impedance, put a resistor between the radio and the transformer, something like 100 ohms or more, as protection against MURPHY. It will also let you run the volume control a bit higher... then, use a simple resistor voltage divider on the output. That will attenuate the signal to a useful level, while at the same time attenuating the amplifier noise. :)
The UPS is a good idea... unless what you're using is a good old fashioned analog car radio. :)