Can I use a 7.5V@700mA power supply with a device listed as requiring
a 7.5V@500mA power supply?

As I understand it, the 700mA is the maximum current draw that a power
supply can handle before it pops the circuit (see the fact that you
can plug a 65W light bulb into a circuit rated for 20A.)

A device has a given resistance in Ohms, and requires a specific
Voltage for the device to function. The current draw is dependent on
the device's resistance and the voltage applied to the device, not the
power supply. The resistance is a fixed hardware limitation. The
voltage is a known quantity, which the device's parts are rated for.
The current draw of the device is the ratio of the known voltage over
the measured resistance of the device. This is constant for constant
voltage.

You'll potentially blow a power supply rated lower than the amp draw
of the device. Higher power supply amperage just means the device can
draw more if needed.

You can do so without harming the power supply. However, if the supply
is *un*regulated, the voltage may rise above that stated when less
than the stated current is drawn, which might harm the appliance. It
would be safer to use a "regulated" power supply, where the voltage
will not rise above that stated.

Owain