Kat,
This is the right approach, using the Sequence command. It would really be a nice contribution to have a good Bayesian of such an important site.
Sometimes you can make the most of old dates, despite their problems – these look like they are in fact in sequence, a good sign that some information can be gleaned from them. Your basic model looks good. Instead of prioritizing high C and Z indices, I would prioritize the priors, that is, the stratigraphic information you're building into the model. A model that more accurately reflects the depositional sequence, despite lower indices, will have results that are closer to the actual dates. I would go back to the profiles and see if you can add more priors, for example, can you assume in some cases that the samples from the lower part of a layer were deposited before those from the middle or upper parts? Sometimes you can really improve on dates with overlapping error ranges (they might even seem inverted based on the medians) if you can confidently put them in sequence.
Are there stratigraphic breaks where you could introduce a Boundary between phases? It used to be more common to run samples twice or even send pieces of the same sample to different labs (you can use R_Combine for such cases). Excavators sometimes re-dated strata with samples from the same depositional events (you can use Combine for such cases).
Are the dates associated with diagnostic artifacts that are from a known date range (based on dates from other sites, for example)? This can also help constrain the large error ranges you have.
Any chance these dates were published in as a date list in Radiocarbon? I have found that sometimes these date lists have much better information that even the excavators provided. Are there any more recent dates that you could associated with one of these strata? That would be great information to include in the model.
It seems some of these details have been discussed recently (Waters and Stafford) that you'd have to consider in such a model:
The authors bring up a significant issue (does anyone know if this can be dealt with in OxCal??)
The alkali-soluble fractions (humates) from two of the dated charcoal samples from unit IIa were dated. In one case the charcoal yielded a date of 13,270 ± 340 14C yr BP (SI-2488) while the alkali-soluble humate fraction yielded a date of 19,800 ± 280 14C yr BP (SI-2488a). A second charcoal sample yielded an age of 16,175 ± 975 14C yr BP (SI-2354) and the soluble humates from this sample were 28,100 ± 800 14C yr BP (SI-2354a). These charcoal-humate date pairs indicate the presence of older soluble carbon, as the alkali-soluble fraction typically dates younger than the charcoal fraction (Haynes 1980).
Another suggestion would be to include First, Last, and Span queries within each phase – this can be useful information you couldn't otherwise guess at. Even if the modeled medians are similar to the calibrated medians (with no model), in most cases they will have much smaller error ranges, which is a great thing about running them through a Bayesian model. This always better than using individual dates (especially uncalibrated ones).
Hope this helps
Erik