FWIW, Google owns .gle, and I emailed both Sundar Pichai and Charleston Registry, but no response of any kind.

My startup is called MedAngle, and we'd love to get medan.gle, but it just left a sour taste in my mouth. Some of these processes are giant black boxes.

I don't think Sundar is likely to go through with your request personally. Your best bet might be if you know an internal engineer working close to their domain management, but even then I'd doubt they'd register it for an external startup. There are currently 21 domains under gle, all related to Google products.

Google is the biggest squatter. https://captnemo.in/tld-squatting/