Amy,
     I am guessing that in using the word "breastshields" you are referring
to what I always call "Nipple Shields". Too often stores and moms hear the
word Breast, and confuse breast SHELLS and breastshields, so I use "Nipple
Shields"  to avoid any further confusion. Breast shells, or hobbit shells, or
milk cups can work for inverted nipples. When Nipple shields are used,
usually the thin silicone ones are associated with better milk transfer, and
stimulation. I have seen a few LCs cut a small hole in the shield and feed
the tube through the hole so baby nurses at breast on the shield, and gets
the tube as well. I have seen Laura Best, NYC do this, but I don't know if
she or her colleagues are online. Other experienced LCs could better comment
on the specifics of this, but thought I'd mention it anyway. Judy Fram,
Brooklyn, NY