> adding 2 dummy regressors for a different baseline between the two days (in addition to the polynomial fits for each run)

It does not make sense to model the average effect for each day in this context. Keep in mind that you've already accounted for the slow drift effect (with polynomials) which includes the intercept (or baseline) for each run. Therefore I fail to see your rationale for a baseline for each day. If you really want such a baseline per day, you could simply obtain the average of the baselines across those runs within each day. However, I would not do that. Remember that the effect estimates in FMRI data can be interpreted as changes *relative* to the baseline, but the baseline value itself is not interpretable because it's just a calibrated number (which should be around 100).

Yes, the same logic applies to your third model.

Gang