The observational link between long gamma-ray bursts (GRBs) and broad-lined stripped-envelope core-collapse supernovae (SNe Ic-BL) is well established. Significant progress has been made in constraining what fraction of SNe Ic-BL may power high- or low-luminosity GRBs when viewed at small off-axis angles. However, the GRB–SN connection still lacks a complete understanding in the broader context of massive-star evolution and explosion physics. Models predict a continuum of outcomes for the fastest ejecta, from choked to ultrarelativistic jets, and observations from radio to X-rays are key to probing these scenarios across a range of viewing angles and velocities. Here, we present results from a coordinated radio-to-X-ray campaign targeting nearby (z ≲ 0.1) SNe Ic-BL designed to explore this diversity. With eight new radio-monitored events and updated data for one previously observed SN, we further tighten constraints on the fraction of SNe Ic-BL as relativistic as SN 1998bw (GRB 980425). We identify SN 2024rjw as a new radio-loud event likely powered by strong interaction with circumstellar material, and add evidence supporting a similar interpretation for SN 2020jqm. We also establish new limits on the properties of radio-emitting ejecta with velocities consistent with cocoons from choked jets, highlighting SN 2022xxf as a promising cocoon-dominated candidate. These results refine our understanding of the continuum linking ordinary SNe Ic-BL, engine-driven explosions, and GRBs, and contribute to building a sample that will inform future multimessenger searches for electromagnetic counterparts to high-energy neutrinos.