Model parametric, event based fMRI task with missing data?

I have a parametric, event based, sparse fMRI task (TR=4 sec). Unfortunately, the parameter I’m interested in using as the parametric regressor value is noisy or outright missing in some of the volumes. It was a response from the subject- the subject responded but our recording equipment and/or post processing algorithms for extracting that value intermittently fail, so I don’t have the value despite knowing that they did the task in some fashion. I have a main effect of task variable, so that’s accounted for.

My question, should I model the dropped volumes as outlier volumes with an unconvolved HRF response just like outlier volumes and motion regressors from art are not convolved with the HRF, or should each missing volume be its own regressor and convolved with the HRF? I lean towards modeling each volume as its own regressor just like an unconvolved art outlier because even though we know partial information (we know about the other regressors of interest) we are missing complete information. The most conservative approach is to just flag the whole volume.

Follow up: how to insert these as additional outliers?
I believe I can make an intermediate node on Ln 1033 that goes from art to MyNode to modelspec in which I modify the outlier files.
Bids/openfmri code here: https://github.com/gciccarelli3/openfmri/blob/master/subject_level/fmri_ants_bids.py