There isn't really a lot of research specifically on babies with sensory issues, but there's one sub-category of babies with sensory issues that has been looked into quite thoroughly: Premature babies.
Preemies aren't ready for the sensory bedlam of the average hospital; but they often need hospital care to survive. Their developing brains are meant to be in the dark, warm environment of their mother's uterus, where sounds are muffled and movements are slow and cushioned and everything around them is soft.
It's been discovered that premature babies will develop better, be less stressed and healthier, if their environments are made soft, dim, and warm. Many modern NICUs have cocoon-like incubators for preemies. The soothing effect of skin-to-skin contact and the sound of another human being's heartbeat is also well-known. Sick infants and preemies who are well enough to leave their incubators at all are often held under a parent's shirt, directly against the skin. I have even heard of people raising orphaned kittens this same way (kittens are essentially born premature, unable to hear or see or regulate their own body temperatures; so they face many of the same obstacles as human preemies).
From that research, I think we could make the preliminary guess that full-term babies who have sensory issues would probably benefit from the same sort of quiet, soothing environment that is provided for preemies, and that interaction with parents will be most soothing if it is low-key, physical contact with more rocking and swaddling than jiggling and tickling. That way, the child can have uncomplicated sensory input to practice on, and the maturing nervous system can become more efficient at its own pace rather than being overloaded by too much stimulation.