Jasmine is recommended for labor. Neroli, too. Rose Absolute. I know these are expensive oils, but birthing is the kind of experience that might call for something extraordinary and some women might choose them, if they are affordable. Blending 5% in jojoba or other carriers would make the expensive oils more accessible
Also, for people who respond well to outdoor fragrances: Spruce, Pine, Cedarwood, Fir or Spruce/Ylang Ylang. Pine also has anti=bacterial properties, etc. and so on.
My main concern is that the birthing administrator should know that sniffing e.o.'s and aromatherapy are not just about smelling good things. Inhalation is actually similar to application on the skin, in that the e.o.'s can enter the bloodstream that way. Diffusers (similar to nebulizers) are used by aromatherapists to deliver therapeutic e.o.'s. (My first positive experience of this use was with pine, spruce and cedarwood. I'd had a bronchial cold/illness for three weeks and recovered after diffusing these organic e.o.s during the night for several nights.)
I'm curious about the stick bars. Is there a reason why the administrator is most interested in that packaging/delivery of fragrance?
Rosemary increases bp, so that is one you might rule out, with the possible of exception of low bp.
Whatever you do, I'd suggest a formal consultation with a licensed, certified clinical herbalist and aromatherapist.
Here's a website you might like for its therapeutic quality oils and detailed information. The customer service is unbelievable and the administrators are aromatherapists: anandaapothecary.com. They test their oils well.
Good luck and keep us posted on your project!