After having been locked for 3+ hours, I started a "sensing function only" calibration measurement following the instructions on the TakingCalibrationMeasurements wiki. This measurement took ~30 minutes after taking H1 out of Observing mode and into NLN_CAL_MEAS.
Attached are a screenshot of the calibration monitor screen prior to the measurement and the generated calibration report: /ligo/groups/cal/H1/reports/20230616T161654Z/H1_calibration_report_20230616T161654Z.pdf