Help with emulating the "New" button on a related list in SF here in Skuid for custom Objects

That is absolutely possible. Just make models for the children records and give them a condition “field from another model” to pull in the ID of the parent record into the appropriate place.   Check out this tutorial that walks you through building a page where Parent and Child records are created on one page:  http://help.skuidify.com/m/components/l/109459-create-parent-and-child-objects-on-the-same-page