Yes, you can use several item types in one itemtype attribute, as long as they are from the same vocabulary. See Microdata: itemtype:
The itemtype attribute, if specified, must have a value that is an unordered set of unique space-separated tokens that are case-sensitive, each of which is a valid URL that is an absolute URL, and all of which are defined to use the same vocabulary.
But note that then all properties (itemprop values) need to be defined for all the specified item types. So you cannot say that a particular property should belong only to a particular item type.
So you’d still have the same problem. In your case, you should either use correct nesting, or you might use the itemref attribute to add properties to the corresponding items that are scattered on the page.
FWIW, the schema.org vocabulary also defines the additionalType property. This can also be used to specify additional item types from other vocabularies. But this doesn’t allow you to use the properties from the additional item type.
