I've had a similar event in a Pa28R (totally my fault as I had forgotten to latch the door - a classic getthereitis case). What surprised me about your story FK73 is that the noise of an open door didn't alert you to the problem. The wind noise was so loud in my case I could barely hear the radio at 100 knots.
The doors on a PA28R and a PA38 are very different
On a PA28 the top latch really pulls in the whole of the top half of the door. Flying without it latched causes a lot of wind noise through a gap of around half an inch which runs about a third of the length of the door, including the front section of the door which is exposed to the airflow.
In a PA38, the top latch really just pulls in the very top of the door, which actually curves over the top of the fuselage. It can leave a gap as small as a quarter of an inch, although could be much larger depending on how well the door fits. This gap is nowhere near as exposed to the airflow as it would be in a PA28, therefore creates a lot less noise. One could easily fly all day with both top latches in a PA38 undone and be none the wiser.