This smallest autocatalytic strand you talk of, with 30 amino acids... is that a computer generated model?
Nope.
See
http://www.asa3.org/archive/evolution/199705/0014.html.
The authors show that a 32-amino-acid peptide, folded into an alpha-helix and having a structure based on a region of the yeast transcription factor GCN4, can autocatalyse its own synthesis by accelerating the amino-bond condensation of 15- and 17-amino-acid fragments in solution
And I think "well supported" means 20+ years of experimental results that support the theory.