How do I know if I fried my Z80?
Putting the Z80 upside-down it's not a good thing, but the Z80 power pins are placed in a way that don't make flows reverse current (11 - 29). Unlucky this cannot give us that the poor and old CPU, even if survived to the time, will continue for the future .... it can be 'tired' about the injury and decide to abandon this cruel world.

For the clock you can use a simple 74LS14 (Schmitt trigger inverter) instead of CD 4093 that is a CMOS, not the best to drive this kind of CPU (with input impedance similar more to a TTL or LS IC than a CMOS).

To investigate more, without to go in the deeps of this archaeological device, consider to test if there are some change in the /MREQ /RD and /RFSH. You can have an help measuring the frequencies at these pins or trying to drive an high impedance headphone with a capacitor in series.