As one paper in a series reporting on a large reverberation mapping campaign of super-Eddington accreting massive black holes (SEAMBHs) in active galactic nuclei (AGNs), we present the results of 10 SEAMBHs monitored spectroscopically during 2015-2017. Six of them are observed for the first time, and have generally higher 5100 luminosities than the SEAMBHs monitored in our campaign from 2012 to 2015; the remaining four are repeat observations to check if their previous lags change. Similar to the previous SEAMBHs, the Hβ time lags of the newly observed objects are shorter than the values predicted by the canonical RHβ-L5100 relation of sub-Eddington AGNs, by factors of ∼2-6, depending on the accretion rate. The four previously observed objects have lags consistent with previous measurements. We provide linear regressions for the RHβ-L5100 relation, solely for the SEAMBH sample and for low-accretion AGNs. We find that the relative strength of Fe ii and the profile of the Hβ emission line can be used as proxies of accretion rate, showing that the shortening of Hβ lags depends on accretion rates. The recent SDSS-RM discovery of shortened Hβ lags in AGNs with low accretion rates provides compelling evidence for retrograde accretion onto the black hole. These evidences show that the canonical RHβ-L5100 relation holds only in AGNs with moderate accretion rates. At low accretion rates, it should be revised to include the effects of black hole spin, whereas the accretion rate itself becomes a key factor in the regime of high accretion rates.