Just puzzled as to the desire to size down from a 5” phone. I assume you want to carry a phone ?, useful if you get hurt, have a mechanical ?. I went from a Motorola flip phone to assorted iPhones, current an Otterbox case. Not seeing an issue in a back pocket in a road ride and inside my CamelBack on mt. bike rides. Re-think that and all your searching is over as a smartphone pretty much does what you want using a lot of choices in free apps.
Just a thought.