Basically what you're doing when going from natural gas to LP is changing to a smaller orifice to allow for the higher pressure supplied by the 'bottled' gas. Natural gas supplies typically run around a pressure of 5.5 inches water column, while LP runs at twice that pressure, averaging around 11 inches. The orifice through which the gas travels to the burner must be smaller to accommodate this difference.
I am sorry, we do not carry Hotpoint prats. We only sell commercial parts and it looks like your stove is for residential use. I recommend calling the manufacturer to get the correct part.
I am sorry, Brinkman is a residential brand that we do not carry. I recommend contacting the manufacturer about how to reach a higher temperature with your unit.