A globally consistent height reference system is vital for monitoring physical heights and enabling diverse geodetic applications. In practice, it shall be realised through the International Height Reference Frame (IHRF). Using clock networks, regional and national height systems can be unified in a novel and unique way to form the IHRF. In this study, we simulate the unification process for two regions - Europe and Brazil - using such a clock-based approach. An a priori height system is selected and subdivided into multiple local height systems (LHS), with complex error parameters introduced (including vertical offsets and systematic tilts) to simulate real-world discrepancies. A closed-loop simulation is performed using a joint adjustment that includes optical clock observations, enabling the estimation of the error parameters and the unified heights. High-performance optical clocks, with fractional frequency uncertainties between 10-17 and 10-18, are assumed. Multiple sites in each LHS are selected as possible clock locations, arranged in a reduced link configuration consisting of master clocks and local clocks. Clock connections are modelled using optical fibre links for local connections and free-space links for inter-LHS master connections. Realistic simulation of clock observations accounts for various error sources in the measurement and analysis process, including clock noise, tidal correction errors, and link uncertainties. The impact of the clock distribution is analysed, and an optimal configuration is identified that minimises the standard deviations of the estimated error parameters and improves the overall unification accuracy. Additionally, the study examines the robustness of the unification under conditions such as the presence of outliers and temporal correlations between common clock observations. The results demonstrate that, under optimal conditions and with clock uncertainties at the 10-18 level, a unification accuracy of 1-2 cm is achievable. Furthermore, the resulting unified heights can be related to the global geoid with an uncertainty of approximately 3 cm.