I am not sure I understand that schematic it doesn't use conventional symbols.
I suspect the transistors aren’t designed to carry that much current so I need a higher rating transistors
They are not, only about 600mA which is nothing for a motor of that size.
Could you list a higher power (Voltage and Current) rating transistors which can equivalently replace 2N2222s
I would not be surprised if there were not thousands of these. In fact with this current then a transistor is not the best solution and you need a logic level FET. It depends on where you live what is available in your location. Find a suppler and look for an n-channel logic level FET.