(I think that your relationships are all actually, reading left-to-right, one-to-many, but you have drawn them as many-to-many.)
If you start with the Parts Table and have relationships like this:
Parts:_kp_PartID ---> LineItems::_kf_PartID --> and then LineItems::_kf_PO_ID --> Purchase Orders::_kp_PO_ID
and then draw a portal in the Parts Layout based on the end of that relationship (Purchase Orders) and put the fields you want in the portal, does that not give you the list of POs you want?
Ah I figured out what I was doing - I actually have another table occurrence of Parts in this relationship I'm using. The layout is for the first table occurrence - which isn't in that relationship.