You won't need to stream all the recordings,. Typically only one or two frames (images) from each event will be sent to Rekognition. And you can downscale them beforehand to reduce the size.

For the non-detected people - you'll have to increase the sensitivity in the Monitor (= camera) settings in ZoneMinder. If you've got it set to Outdoor (12.5%) it may be too much, try reducing it to Indoor (6.75%) or even lower. You'll probably get more false alarms but also should get the alert for the persons walking by.