Switching propane bbq to natural gas
Just like with kitchen cookers (ovens, hobs, grills), which have a different set of jets for lpg or natural gas, using inappropriate jets won't work properly. Obviously your bbq is jetted for lpg, and works well on that. However, since most gas bbqs are designed for lpg, you probably won't find jets for natural gas that will fit your bbq.
Also, the regulator will possibly be producing a pressure that won't do the job. Best to question the manufacturers/retailers of your bbq - you may be lucky, but somehow, it's doubtful. Bbqs are usually designed to be portable/moveable, and being fixed to a gasline from a house isn't envisaged.