Mechanically, the honest answer is that published stability data for these specific molecules in a research-grade presentation essentially does not exist, so what you get is extrapolation from the licensed formulations and from general peptide chemistry. That extrapolation is reasonable. It is still extrapolation.
The 28-day figure for a reconstituted preserved vial is microbiological, not chemical. Chemically, a well-behaved peptide at 5 mg/mL at 4 °C will typically lose well under a per cent of content per month. The reason to respect the date is bioburden, and bioburden is a function of how many times you have opened it, not of the calendar.
Stated carefully, aggregation is the failure mode that reverse-phase HPLC is worst at detecting, because a large soluble aggregate may not elute at all and an insoluble one is filtered out during sample preparation. If your purity result comes back normal but the vial looks hazy, believe the vial. Size-exclusion chromatography is the method that sees this.
The Arrhenius relationship underpinning accelerated stability testing is the basis of ICH Q1A, which is why accelerated studies at 40 °C and 75 per cent relative humidity are used to predict shelf life at 25 °C. The same relationship lets you reason about a warm transit lane, with the same caveats about extrapolation.
Minimise transitions rather than minimising temperature. One freeze and one thaw is fine; five is a different question.