I am looking for publications demonstrating the sedimentation VS subsidence rates in minibasin settings and the controlling factors. Sedimentation type and architecture would be helpful as well.
Begin with what causes minibasins. Where salt diapirs are involved, the variables are many. Search 'halotectonics, diapir/salt dome emplacement etc. These can be very complex environments.
They are indeed very complex systems, depended on many variables.
A lot of research has been carried out, with many outstanding works enlightening this still obscure matter.
Though, I haven't found yet any paper who deals and characterizes mini basins in terms of stratigraphy or paleoenvironment. Maybe I'm not aware of possible case studies, or modelling results. So the question remains