Purification of primary amines using Schiff base immobilization
Let's take your questions one at a time.


Are there any alternative ways to purify primary amines from a complex mixture that I am unaware of?


Your end application is LC-MS.  There are plenty of papers on amine-specific derivatization methods for metabolome analysis. For example, there is one by Zhao et al. [1]. Instead of purifying the primary amine metabolites and isolating the purified mixture as a separate step, they just rely on the analytical instrumentation to be able to identify primary amines from their derivatization pattern.
Alternately, as suggested in the comments by @Waylander, you could acidify the sample to form ammonium ions, and then pass the sample through a cation exchange column, where only positively charged ions will bind.  As you noted, this will not be perfectly selective for primary amines, because species like quaternary ammonium salts etc. will also be retained.
You could combine the derivatization approach with the SCX approach, of course.  If you chose a primary-amine-selective derivatization, you might get a selective method.  At some point, however, the complexity of the method will become a drawback.


Have anybody else, published or unpublished, used Schiff base chemistry to purify primary amines?


Well this question is impossible to answer for the unpublished case.  I couldn't find any published methods in a quick search, which makes me suspect it is not the best approach to your problem.  But I could be wrong of course!


What would be your odds that this could work? Is it worth pursuing?


Unanswerable without data.  I suspect that secondary amines, at least some times, will also react with the aldehydes to form Schiff-base-like iminium cations, and may also be selected by your proposed method.


Any ideas for improvements?


I think derivatization, without separation or isolation of the amines, would be an attractive direction for you to consider.  The paper I linked, its references, and the papers that reference it might be good starting places.
Reference

Zhao, S.; Li, H.; Han, W.; Chan, W.; Li, L. Metabolomic Coverage of Chemical-Group-Submetabolome Analysis: Group Classification and Four-Channel Chemical Isotope Labeling LC-MS. Anal. Chem. 2019, 91 (18), 12108–12115. DOI: 10.1021/acs.analchem.9b03431.