Yes, you can use a power supply with higher amperage, as long as the output voltage is rated 24AC.
It’s a common misconception that a higher amperage (current rating) will damage the circuit: the current rating (500mA or 1amp) simply means that the power supply is capable of delivering that much current if it’s needed. The actual current draw depends on how much the circuit needs. For example, if the circuit only needs 700mA, that’s how much current the adapter will deliver (assuming its current rating is more than 700mA). If the current rating is lower, the consequence is that the adapter cannot sustain the output voltage, so either the voltage will drop significantly below 24VAC or it will simply collapse causing the controller to reboot.