Thank you for the insight. Would you be willing to elaborate a bit on finding a good match for advisor, and perhaps any thoughts on approaching someone about exploring an advisorship?
First step is to be acquainted with their previous research. Understand the direction they are taking and what their interests are. Find advisors whose work you think you can build on through your PhD. Write down what you are interested in working on and how it relates/expands/builds on your potential advisor's. Then contact them sharing just that and start having a conversation - they will surely have feedback and ideas for directions that your research could take.