Clock network delay + internal cell delay > Minimum timing requirement

I don't know whether you'd have to make an adjustment for the clock inversion. In most cases TimeQuest does what you need automatically, but in some situations you need to tell TimeQuest the clock edge you care about.

It sounds like you now have a source-synchronous setup for which you can use the -reference_pin method. Instead of -reference_pin, you can create a generated clock on your new clock output device pin and use that generated clock in the set_output_delay constraints.