I read your post again.

How can I use the entire timeseries to do the regresson if this is a live neuro feedback run?

Firstly, the first time we collect data is about 27 TRs into the run. The following TRs have not been generated yet. So I don't see how I can use the full run.
Secondly, if we did this but "backwards"
First time we calculate something: use TR 0 up until last TR to include (e.g. 0-27)
and so forth.
In the later feedbacks, we would get TR 0 - 428.
This would take more time. To get 400+ niftis. Concatinate, scale and run a regresson. Would take more than the 3 s we allow ourself as a delay betwen a scanned event and the feedback.

Long story short:
We can skip motion correction.
And if we find improments (reduction of activity in the chosen region over time) we can do the motion corrected version offline aftwerards and see if it stil holds up?

Best,
Robin