You're probably making engine noise during your extended cranking, it's just a different frequency and mixing in with the starter noise.
When fuel injection first came out, cars started right up. Then Ford engineered their 4.6 to take a minimum of four revolutions to build oil pressure and everyone else followed suit. (The start-stop cars out now start faster on warm restarts.) Why four? IDK, but it's "about right" and has been the standard for 30 years. I'd start the jeep normally and get used to the rattle.
Your tazer sounds cool, though. The engine is at its best behavior at its thermostat temp; shedding radiator, transmission, and underhood heat early won't hurt anything aside from maybe wearing out the fan motor.