Solo Agency: We really want to ship it soon but the issue is that Tidycal doesn't provide any way to let the "host" page know that the event has been scheduled.

I have contacted Tidycal support for the same. If you are a user of Tidycal can you also drop their support a message regarding the same? May be this will speed up the process.

The other embed solutions like Calendly, Cal.com and SavvyCal provides this feature.