Should I push a 15-amp extension cord to its limit?

No, don’t push a 15-amp extension cord to its limit. A 14.5-amp continuous draw is too close to the 15-amp rating; the safe rule for continuous loads is 80%, meaning 12 amps max. Running 14.5 amps through a 15-amp cord creates heat buildup that can soften the jacket, degrade insulation, and risk fire. Get a 12-gauge cord rated for 20 amps, or plug the device directly into the wall.