We study the consistency and consistency strength of various configurations concerning the cardinal characteristics $\mathfrak {s}_\theta, \mathfrak {p}_\theta, \mathfrak {t}_\theta, \mathfrak {g}_\theta, \mathfrak {r}_\theta $ at uncountable regular cardinals $\theta $. Motivated by a theorem of Raghavan–Shelah who proved that $\mathfrak {s}_\theta \leq \mathfrak {b}_\theta $, we explore in the first part of the paper the consistency of inequalities comparing $\mathfrak {s}_\theta $ with $\mathfrak {p}_\theta $ and $\mathfrak {g}_\theta $. In the second part of the paper we study variations (...) of the extender-based Radin forcing to establish several consistency results concerning $\mathfrak {r}_\theta,\mathfrak {s}_\theta $ from hyper-measurability assumptions, results which were previously known to be consistent only from supercompactness assumptions. In doing so, we answer questions from [1], [15] and [7], and improve the large cardinal strength assumptions for results from [10] and [3]. (shrink)