Determining the strength of the ancient geomagnetic field is vital to our understanding of the core and geodynamo, but obtaining reliable measurements of the paleointensity is fraught with difficulties. Over a quarter of magnetic field strength estimates within the global paleointensity database from 0 to 5 Ma come from Hawaii. Two previous studies on the SOH1 drill core gave inconsistent, apparently method‐dependent paleointensity estimates, with an average difference of 30%. The paleointensity methods employed in the two studies differed both in demagnetization mechanism (thermal or microwave radiation) and Thellier‐style protocol (perpendicular and original Thellier protocols)—both variables that could cause the strong differences in the estimates obtained. Paleointensity experiments have therefore been conducted on 79 specimens using the previously untested combinations of thermal‐perpendicular and microwave‐original Thellier methods to analyze the effects of demagnetization mechanism and protocol in isolation. We find that, individually, neither demagnetization mechanism nor protocol entirely explains the differences in paleointensity estimates. Specifically, we found that non‐ideal multidomain‐like effects are enhanced using the original Thellier protocol (independent of demagnetization mechanism), often resulting in paleointensity overestimation. However, we also find evidence, supporting recent findings from the 1960 Kilauea lava flow, that microwave‐perpendicular experiments performed without partial thermal remanent magnetization checks can produce underestimates of the paleointensity due to unaccounted‐for sample alteration at higher microwave powers. Together, these findings support that the true paleointensities fall between the estimates previously published and emphasize the need for future studies (thermal or microwave) to use protocols with both partial thermal remanent magnetization checks and a means of detecting non‐ideal grain effects.