This paper presents a novel topology-aware dimensionality reduction approach aiming at accurately visualizing the cyclic patterns present in high dimensional data. To that end, we build on the <italic>Topological Autoencoders</italic> (TopoAE) (Moor et al., 2020) formulation. First, we provide a novel theoretical analysis of its associated loss and show that a zero loss indeed induces identical persistence pairs (in high and low dimensions) for the 0-dimensional persistent homology (<inline-formula><tex-math notation="LaTeX">$\text{PH}^{0}$</tex-math></inline-formula>) of the Rips filtration. We also provide a counter example showing that this property no longer holds for a naive extension of TopoAE to <inline-formula><tex-math notation="LaTeX">$\text{PH}^{d}$</tex-math></inline-formula> for <inline-formula><tex-math notation="LaTeX">$d\geq 1$</tex-math></inline-formula>. Based on this observation, we introduce a novel generalization of TopoAE to 1-dimensional persistent homology (<inline-formula><tex-math notation="LaTeX">$\text{PH}^{1}$</tex-math></inline-formula>), called TopoAE++, for the accurate generation of cycle-aware planar embeddings, addressing the above failure case. This generalization is based on the notion of <italic>cascade distortion</italic>, a new penalty term favoring an isometric embedding of the 2-chains filling persistent 1-cycles, hence resulting in more faithful geometrical reconstructions of the 1-cycles in the plane. We further introduce a novel, fast algorithm for the exact computation of <inline-formula><tex-math notation="LaTeX">$\text{PH}^{}$</tex-math></inline-formula> for Rips filtrations in the plane, yielding improved runtimes over previously documented topology-aware methods. Our method also achieves a better balance between the topological accuracy, as measured by the Wasserstein distance, and the visual preservation of the cycles in low dimensions.