Is there such a service/API that could help with this? Services like Calendly are great, but it feels presumptuous to send their link, and often inappropriate.
Only closest possible workflow is this 1. Create a public calendar link in Google Calendar that shows your availability 2. Create an event with your preferred time and a description : "Feel free to change the time of the meeting. Here's my availability: {public calendar link}" 3. Invite the person you want, make sure they have permission to edit the event