The Elgato box will accept a 1080p60 input, though it will capture at only 30fps (which is fine). I suspect there's just something weird about the HDMI output of the adapter/scaler I bought, and ...

HDMI has limitations, though, and isn't always the perfect choice. For example, your TV likely has HDMI 1.4 connections, which max out at 3,820x2,160-pixel resolution at 30 frames per second.