I don't know if you have come across the Folch method - very old but variations on it are still very much in use today.  Folch et al (1957) Journal of Biological Chemistry, 226: 497.

Bligh and Dyer also produced a one-step method (Bligh & Dyer (1959) Canadian Journal of Biochmistry and Physiology, 37: 911-917).

See also Iverson et al (2001) Lipids, 36(11): 1283-1287 for a modern comparison. 

GC-MS should show up most of your fatty acids, certainly up to C22, and will distinguish the unsaturated ones as well with the correct programme and column.  However the very short chain ones are not usually detected as they elute with the solvent front.  They are also very volatile and can get lost in the sample prep if too much heat is applied.  I have seen down to C5:0 with a standard split-splitless set up but as I'm mostly looking at very old samples where very short chain fatty acids don't survive, I've never tried to look for anything smaller.

Thanks for the papers to look into. I skimmed through them in my spare time here and noticed that they used tissue that has water content which helps produce the monophasic solution when the tissue is homogenized. Are you aware of if the tissue does not contain much if any water, such as a died down stool sample, would these methods work or would the monophasic solution not be made at all or as well because there is none to very little water in the tissue sample?

I know that a colleague of mine uses an adapted acid methanolysis method on very dry, partially carbonated, archaeological residues and ceramic (both of which are usually completely dry) with good results.  The method has been described in Correa-Ascencio & Evershed (2014) Analytical Methods 6(5): 1330-1340.  I know the matrix is different but it is usually very dry, which might be reasonably equivalent to your situation.  I have used a slightly adapted method on bone as well.