Michael, when we wish to calculate peptide hydrophobicities we use the Wimley–White whole residue hydrophobicity scale. We have found our nano HPLC retention times correlate well (>90% of the time) with this scale and we use the values as set out in this table https://www.cgl.ucsf.edu/chimera/docs/UsersGuide/midas/hydrophob.html 

Hope this is of use to you.

Hydrophobicity scales, are experimentally determined transfer free energies for each amino acid, These are essential for understanding the energetics of protein-bilayer interactions. Two scales are needed, one for the transfer of unfolded chains from water to bilayer interface and one for the transfer of folded chains into the hydrocarbon interior. The most important feature of practical scales is the inclusion of contributions of the peptide bonds for the obvious reason that whole residues, not just sidechains, partition into membranes. That is, the scales must be whole-residue scales. We have determined such scales for POPC bilayer interfaces (1) and for n-octanol (2) using two families of peptides: host-guest pentapeptides of the form AcWL-X-LL, for determining sidechain hydrophobicities, and the homologous series AcWLm(m = 1..6), for determining peptide bond hydrophobicities

I notice this question just now. I am not sure whether it is of interest to the initial person who asked this question anymore, but for those wondering I will try to answer this not so easy to answer question.

As stated in the question itself: there is no such thing as the best hydrophobicity scale. All frequently used scales are based on different principals. Either theoretical, based on the distribution of your substance (amino acid or peptide etc.) in the present hydrophobic or hydrophilic phase, based on extraction of in vivo or in vitro results etc.

It is important to realise that several bioinformatics tools are based on different scales, for example Fauchere & Pliska (Heliquest), Eisenberg et al. (Hydrophobic Moment Plot), Kessel & Ben Tal (MCPep).

See for a little comparison (and references), in the corresponding paper you can find an example of a discussion on the limitations of some of these scales:

Data keller3biotech2015suppl.docx

Obviously in general there is consensus about most amino acids on whether the need to characterised as hydrophobic or not. However tryptophan for example is an interesting example which role in protein-lipid interactions is based on experimental findings much more prominent than the majority of hydrophobicity scales seems to indicate.

See for some examples for this:

https://pdfs.semanticscholar.org/2826/a42a76200f3a5a08019de551dd138ffa1d3c.pdf

Article Analysis of the Role of Interfacial Tryptophan Residues in C...

Amino acid hydrophobicity scale

https://www.sciencedirect.com/science/article/abs/pii/0022283682905150

very popular and necessary. Everyone using this scale understands that it differs from the actual hydrophobicity of amino acids in a cell of a living organism. Micelles of ionic surfactants show that the energy of the zero point of water contributes to their existence up to 40%. This environment of the state of water is closer to the cell of a living organism and can be used for more accurate determination of the hydrophobicity of amino acids.

Preprint The Role of Zero-Point Energy of Water in Micelle Formation ...

https://www.researchgate.net/post/Can_the_treatment_for_COVID_viruses_and_bacteria_be_fundamentally_changed

https://www.researchgate.net/post/Isotopic_effect_studies_available_in_mice_that_are_not_infected_and_infected_with_COVID

Dear Michael Christopher Beckett to get an overview of this topic, please see this review article entitled "50 years of amino acid hydrophobicity scales: revisiting the capacity for peptide classification". The paper was published in 2016 in the journal Biological Research and is available Open Access.