The spinel compounds MnSc₂X₄ are highly frustrated and candidate materials for vortex-like 3q magnetic states, such as skyrmions, with propagation vectors in the [111] plane. Because of the strong magnetoelastic coupling, we could extract a refined magnetic (H,T) phase diagram for MnSc₂S₄ from ultrasound and dilatometry measurements. We found a variety of magnetic phases, including the skyrmion phase, which is stable down to lowest temperatures. In comparison, we investigated MnSc₂Se₄, having a larger distance between the magnetic Mn³⁺ ions using the same methods. Unlike in MnSc₂S₄, we found no skyrmion phase and overall a lack of sharp anomalies indicative of phase transitions, neither in dilatometry nor ultrasound nor in specific heat and ac-susceptibility data. Motivated by our findings, we performed model calculations, which reproduced the experimentally observed magnetostriction and specific-heat results reasonably well.