I'm surprised it takes more than 1 email each to pick a time.

Offer: Let's have a call. I'll suggest 2pm Tue. If that doesn't work, please let me know any time between 1pm-6pm Tue or 9am-11am Wed.

Response: 9am Wed.

I do think the gmail calendar approach is neater; the only downside being it requires the other party to use google calendar already.