Eremocrinum: Where does it belong in Asparagales?

[caterpillar]

Hi,   

  I'm an amateur botanist who's been trying to figure out how the
family placement of North American plants has changed with the onset
of all this molecular data.  Right now I'm looking everything that
used to be placed in the Liliaceae, and oh what a mess it is!

   I think  I've got all the genera in  place (see below), except for
one.  The monospecific genus Eremocrinum of  Utah and Arizona was
formerly included in the Anthericaceae.  According to the article by 
Mark W. Chase et al [1996.  New circumscriptions and a new family of
asparagoid lilies: Genera formerly included in Anthericaceae. Kew
Bulletin 51(4): 667-680], its position is unknown, although they do
say that the species is  similar to Chlorogalum.  Does that mean that
Eremocrinum  belongs with Chlorogalum at the base of  the Agavaceae? 
Has anyone run the DNA on Eremocrinum?

   Here's what I've come to understand is the botanists' new
understanding of family relationships in the Liliales and Asparagales
(only families & genera  native to North America north of Mexico are
listed):

    Haemodoraceae (Lachnanthes) –  Now placed  in the Commelinales.
    Nartheciaceae (Aletris, Lophiola, Narthecium) – Now placed in the
Dioscoreales.
    Tofieldiaceae (Harperocallis, Pleea, Tofieldia) – Now placed in
the Alismatales.


Order Liliales
   Colchicaceae (Disporum, Uvularia)

   Melanthiaceae (Amianthium, Chamaelirium, Helonias, Melanthium,
Schoenocaulon, Stenanthium, Trillium, Veratrum, Xerophyllum,
Zigadenus)
   
   Liliaceae (Calochortus, Clintonia, Erythronium, Fritillaria,
Lilium, Lloydia, Medeola, Scoliopus, Streptopus,

   Smilacaceae (Smilax)


Order Asparagales
   Orchidaceae
   Hypoxidaceae (Hypoxis)
   Iridaceae (Hypoxis is now in Hypoxidaceae)

   Tecophilaeaceae (Odontostomum)

   Alliaceae (Allium, Nothoscordum)

   Amaryllidaceae (Cooperia, Crinum, Habranthus, Hymenocallis,
Zephyranthes)

   Themidaceae (Androstephium, Bloomeria, Brodiaea, Dichelostemma,
Milla, Muilla, Triteleia, Triteleiopsis)

   Agavaceae (Agave, Camassia, Chlorogalum, Furcraea, Hastingsia,
Hesperaloe, Hesperocallis, Manfreda, Schoenolirion, Yucca)

   Anthericaceae (Echeandia, Leucocrinum)

   Ruscaceae  (Convallaria, Dasylirion, Maianthemum, Nolina,
Polygonatum)