There is no good way to estimate properties using only chemical composition.  The processing (casting, homogenization, hot deformation, cold deformation, and post-forming heat treatment) are so influential that you cannot ignore them.

I am curious why you would go from a
known material to an unknown.  A36 is an
industry standard.  Is it cost only that
you are considering.  The carbon content
range of .05/.33 seems like too great a
variation. I think it would probably compare
to an AISI 1010 steel if you need something
similar for comparison.  Whoever supplies the
material should be able to verify the mechanical
properties for the normalized state which I
assume you are using now.

Mainly Cost.  I do not need the 36 KSI min yield strength.  I could go a little lower.  

The manufacturer gets cobble steel from their vendor but doesn't know what steel it was meant to be.  They do a 13 element analysis on every plate and certify it.  They don't check the material properties.  They have shown some willingness to do a hardness test to each plate.  Would this help in determining the yield strength?  I would like to stay above a min Yield of 25 KSI.

The majority of their plates are down in the .05 % Carbon range.  I probably don't need to go as high as 0.33%  A36 for 3" plate gives a max of 0.27%.

The steels being discussed here are all low carbon steel with various strain levels to adjust mechanical properties.  There should not be a large cost difference among them.  Since 25 ksi is very low strength, you should be able to get a low price from a vendor even if you specify 25 ksi min yield strength in addition to chemistry.

If you are working with a vendor who can't/won't give mechanical property data, and has to be coaxed to provide hardness data, then you are working with the wrong vendor.