I looked up this 1996 paper that you cite. Briefly, the authors study their company’s cation-exchange material, Hyper D, with some peptides obtained from a digest: MAIPPK (A1), MAIPPKK (A2), KNQDK (B1), and NQDK (B2). They consider four alternative factors that could influence retention: 1) Charge-to-mass ratio; 2) Peptide pI; 3) Positional effects (without invoking orientation per se); 4) Hydrophilicity. Observations:
1) The order of elution does not match the pI. One explanation for this is that peptides B1 and B2 have an Asp residue next to a Lys residue, thereby neutralizing the potential retention contributed by that Lys. As one goes to lower pH, the Asp sidechain becomes protonated and the adjacent Lys can then interact with the stationary phase. Accordingly, as pH decreases the retention of B1 and B2 increases as a set relative to A1 and A2. The authors missed this completely.
2) At a pH of 1.5, low enough for the Asp sidechain to be uncharged, standard B1 with a Lys residue at each terminus elutes later than standard A2 where both Lys residues are at the C-terminus. This is consistent with our 2010 paper (which you cited) that finds that tryptic peptides tend to be oriented on a cation-exchange material with the N-terminus facing the stationary phase. At pH 4 and 6 the Asp is charged and B1 elutes earlier than A2. The authors discuss the results from pH 4 only, citing them as a basis for rejecting a role for positional effects. Instead, they ascribe the elution order to hydrophilic interaction, notwithstanding the absence of organic solvent in the mobile phase.
The authors proceeded to invoke some equations, do some model building, and praise the ability of Hyper D to separate peptides of similar charge. Now, a study that only involves some arbitrary set of naturally-occuring peptides has the intellectual rigor of bird watching. To elevate their ideas on retention to the level of a falsifiable hypothesis, the authors should have come up with some test that could demonstrate that they were in fact false if a particular outcome was obtained. In this case, that would have involved something like synthesis of the peptides NQDKK (an analogue of B1 with the Lys residues in the same order as in standard A2) or KNDQK (a different analogue of B1 in which the Asp residue is not adjacent to either of the Lys residues). These peptides would have the same pI and hydrophilic character as B2. If all three coeluted, then that would have ruled out positional [and orientation] effects from the mechanism of separation.
Your summary of our 2010 paper is on target: with multiple charged centers, rigid orientation of the peptide is lost and retention is a function of the net charge. Charge-to-mass issues may play some role. So far, nobody has published anything exploring them; our 2010 paper was the first that demonstrated through experimentation that orientation effects did exist and could account for separation of positional variants. One of our coauthors, Kostas Petritis, does have some nice data on the retention of tryptic petides in SCX as a function of the peptide size and charge. Charge-to-mass effects are evident. You'll have to contact him if you want to get some idea when he's going to publish this; he's currently at TGen in Phoenix.
Figures for pKa of amino acid sidechains in aqueous-organic media: Look up the extensive series of papers by Marti Roses.