The end-to-end connectivity patterns between two points on Earth are highly volatile if mediated via a Low-Earth orbit (LEO) satellite constellation. This is rooted in the enormous speeds at which satellites in LEO must travel relative to the Earth's surface. While changes in end-to-end routes are rare events in stationary and terrestrial applications, they are a dominating factor for connection-oriented services running over LEO constellations and mega-constellations. This paper discusses how TCP-over-constellations is affected by the need for rerouting and how orbital route selection algorithms impact the end-to-end performance of communication. In contrast to the state of the art that primarily optimizes for instantaneous shortest routes (i.e. lowest delay), we propose several algorithms that have route stability and longevity in their focus. We show that this shift in focus comes with vastly improved end-to-end communication performance, and we discuss peculiar effects of the typical TCP-like implementations, taking inspiration from the Starlink constellation in our empirical investigations. The spectrum of algorithms proposed provides a basis for co-designing suitable orbital route selection algorithms and tailored transport control algorithms.