I've got a Q200 and Q120. My real choice is real wood but either of those Weber's does a darn fine job for a go to grill. They run off of full tank pressure but your tapline is after it goes thru the regulator, don't think it works that way, been reported here several times. I use an inline T from between the tank and hose to regulator connection that I run my remote hose to the grill with.
Looks like the video above my comments might offer a solution.
2005 Dodge Ram 2500 5.9L 6 Speed
16" Michelins, Hi Spec Wheels, Max Brake, Carslile Actuator, Equal-i-zer, Dill TPMS. Campfire cook.