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We study theoretically and numerically chirality and saddle-splay elastic constant (K_24) enabled stability of multiple-twist-like nematic liquid crystal (LC) structures in cylindrical confinement. We focus on the so-called radially-z-twisted (RZT) and radially-twisted (RT) configurations, which simultaneously exhibit twists in different spatial directions. We express free energies of the structures in terms of dimensionless wave vectors, which characterise the structures and play the role of order parameters. The impact of different confinement anchoring conditions is explored. A simple Landau-type analysis provides insight into how different model parameters influence the stability of structures. We determine conditions for which the structures are stable in chiral and also nonchiral LCs. In particular, we find that the RZT structure could exhibit macroscopic chirality inversion on varying the relevant parameters. This phenomenon could be exploited for measurements of K_24.