PSR J1227-6208 is a recycled pulsar in a bianry with a massive white dwarf companion. A recent timing measurement from combined MeerKAT and Parkes observations shows the companion mass to be between 1.2 and 1.5 $M_\odot$, very close to the Chandrasekhar, resulting in potential profound physical implications. However, the timing precision is limited by the DM timing noise. We propose regular monitoring of this pulsar with the Parkes UWL receiver in conjunction with MeerKAT observations during the following four years. The joint monitoring will significantly improve the constraints on the Post-Keplerian parameters, with Parkes observations contributing to constrain the DM noise due to its large frequency bandwidth. These observations will be added to the already existing 11-year-long timing baseline, of which the later 5 years already include high-precision MeerKAT data and Parkes UWL data. After four years of further timing with the inclusion of UWL observatiosn, we predict an uncertainty on the masses smaller than 0.01 solar masses based on simulations. If UWL is not included, the mass uncertanites may saturate on their current values.