Hope it works out. Seem like it would be tough to arrive a specific times and temps without knowing your steel. Maybe the part has been around a while and doesn't need hardening. Main thing I'd wonder about is altering the sear due to heating it exposed to oxygen and possible warping.
If you know the steel, depending how you do it, 5 minutes in an electric kiln may not bring the whole part up to uniform temp. It's true that many heat treat recipes call for longer tempering times, but as mentioned it may not have the ability to harden in the first place.
