Good comprehensive article Annie Lowrey.
Raising the minimum wage to $15 has a simple and popular appeal, and as you say the experience of the downside doesn't seem to be as great as many have previously said. So, may be do it.
On the other hand, there may be better ways of achieving the goal of countering poverty in low income individuls and families. Solutions that are perhaps more direct and interfere less with the labor market -- such as cash payments directly into the pockets of those below a certain income. Also, the overhead of running the program would be less.
There is a bigger alternative too. Raising the minimum wage can be wrapped in to a much more comprehensive program to address the whole problem of income inequality. I wrote about this in a number of articles inclding "Wings to Fly -- a Platform for All" -- here on MEDIUM. I would welcome your comments.
There is the popular notion that labor costs are determined by employers -- they are not. They are determined by the market.