I like getting into a nice rhythm, too.
I’ve only GPS’d myself once in a sea kayak over much of a distance and I mesured 4mph over 7 miles in my composite Sea Lion and I was paddling as well as I could at a pace that I thought I could sustain for a couple hours. I could go over 5mph in a sprint, but that wasn’t my objective. I can get my canoes close to 5mph in a sprint, but can’t sustain it long. It was my first time paddling over three miles this year. The water hasn’t been liquid very long.
When I’m out by myself, I’m usually paddling about as fast as I think I can go to for the amount of time I’m planning to paddle without over stressing my poorly conditioned muscles and joints. I’m not lillydipping, I just can’t go any faster for very long without hurting myself.
I’m fairly new to sea kayaking, so I’m sure that my technique is a limiting factor as well as my conditioning and I might not have a big enough motor for the boats I have.
My impression is that you are a pretty experienced and skilled paddler.
We all have different abilities, goals and gear.