R Coronae Borealis (RCB) variables and their non-variable counterparts, the dustless Hydrogen-Deficient Carbon (dLHdC) stars have been known to exhibit enhanced s-processed material on their surfaces, especially Sr, Y, and Ba. No comprehensive work has been done to explore the s-process in these types of stars, however one particular RCB star, U Aqr, has been under scrutiny for its extraordinary Sr enhancement. We aim to identify RCB and dLHdC stars that have significantly enhanced Sr abundances, such as U Aqr, and use stellar evolution models to begin to estimate the type of neutron exposure that occurs in a typical HdC star. We compare the strength of the SrII 4077{AA} spectral line to CaII H to identify the new subclass of Sr-rich HdCs. We additionally use the structural and abundance information from existing RCB MESA models to calculate the neutron exposure parameter, {tau}. We identify six stars in the Sr-rich class. Two are RCBs, and four are dLHdCs. We additionally find that the preferred RCB MESA model has a neutron exposure {tau}~=0.1mb^-1^, which is lower than the estimated between 0.15 and 0.6mb^-1^ for the Sr-rich star U Aqr found in the literature. We find trends in the neutron exposure corresponding to He-burning shell temperature, metallicity, and assumed s-processing site. We have found a sub-class of 6 HdCs known as the Sr-rich class, which tend to lie in the halo, outside the typical distribution of RCBs and dLHdCs. We find that dLHdC stars are more likely to be Sr-rich than RCBs, with an occurrence rate of ~13% for dLHdCs and ~2% for RCBs. This is one of the first potential spectroscopic differences between RCBs and dLHdCs, along with dLHdCs having stronger surface abundances of 18O. We additionally find neutron exposure trends in our RCB models that will aide in understanding the interplay between model parameters and surface s-process elements.