As you said it may not be the heater but it could be the supply line. How far is the heater from the meter and what size line is it? With a 400k BTU heater, you probably need at least a 1" gas supply line. Simply replacing the heater may not solve your problem if the supply line is too small.

Also, measuring the pressure with the heater off does not give you an accurate reading as like with water, gas loses pressure as it moves through the pipes. Since it dips when turned on, it would seem there is a restriction up stream from the heater which would indicate the supply line again.

Another thing to check is the gas filter screen in the heater. When mine was installed, there was a small amount of dirt in the gas line which plugged up the screen. Once it was cleaned it worked perfect.