when we have such separation problems, we use specific "centrifugal filtration devices". Their use is very easy. The have the size of an Eppendorf tube and fit in every normal centrifuge. Inside they have a filter cartridge with a filter membrane, which has a certain size exclusion. As example, Millipore has an Amicon4 with a 300 Dalton cut-off so only your peptide will pass through. Other suppliers have similar devices, where you can select your cut-off of choice. Simply check out for "centrifugal filtration devices".
The content of peptide is more than 1% and hence extraction with solvents like ethyl acetate or dichloro methane, followed by crystallization with hexane should help for purification.
There are several reported methods for the assay.
The methods are selective for the class of peptides. You need to choose from that.