So, like everyone else, I have too wandered down the roads of using doodle, when2meet, zcal and all other 800 alternatives to the problem. Until 5 months back that is, when I found, schej.it; and trust me, it is the best app ever (in my opinion) for finding a time to meet. Allows you to overlay your google calendar, restrict participant visibility, send google calendar invite based on the decided time, everything you can think of.