The supermassive black holes (M BH ∼ 106–1010 M ⊙) that power luminous active galactic nuclei (AGNs), i.e., quasars, generally show a correlation between thermal disk emission in the ultraviolet (UV) and coronal emission in hard X-rays. In contrast, some “massive” black holes (mBHs; M BH ∼ 105–106 M ⊙) in low-mass galaxies present curious X-ray properties with coronal radiative output up to 100× weaker than expected. To examine this issue, we present a pilot study incorporating Very Large Array radio observations of a sample of 18 high-accretion-rate (Eddington ratios L bol/L Edd > 0.1), mBH-powered AGNs (M BH ∼ 106 M ⊙) with Chandra X-ray coverage. Empirical correlations previously revealed in samples of radio-quiet, high-Eddington AGNs indicate that the radio–X-ray luminosity ratio, L R/L X, is approximately constant. Through multiwavelength analysis, we instead find that the X-ray-weaker mBHs in our sample tend toward larger values of L R/L X even though they remain radio-quiet per their optical–UV properties. This trend results in a tentative but highly intriguing correlation between L R/L X and X-ray weakness, which we argue is consistent with a scenario in which X-rays may be preferentially obscured from our line of sight by a “slim” accretion disk. We compare this observation to weak emission-line quasars (AGNs with exceptionally weak broad-line emission and a significant X-ray-weak fraction) and conclude by suggesting that our results may offer a new observational signature for finding high-accretion-rate AGNs.