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We report the results from follow-up observations of two Roche-lobe filling hot subdwarf binaries with white dwarf companions predicted to have accretion discs. ZTF J213056.71+442046.5 (ZTF J2130) with a 39-min period and ZTF J205515.98+465106.5 (ZTF J2055) with a 56-min period were both discovered as subdwarf binaries with light curves that could only be explained well by including an accretion disc in their models. We performed a detailed high-resolution spectral analysis, using Keck/ESI to search for possible accretion features for both objects. We also employed polarimetric analysis using the Nordic Optical Telescope (NOT) for ZTF J2130. We did not find any signatures of an accretion disc in either object, and placed upper limits on the flux contribution and variation in degree of polarization due to the disc. Owing to the short 39-min period and availability of photometric data over 6 yr for ZTF J2130, we conducted an extensive O − C timing analysis in an attempt to look for orbital decay due to gravitational wave radiation. No such decay was detected conclusively, and a few more years of data paired with precise and consistent timing measurements were deemed necessary to constrain $\dot{P}$ observationally.