That's a lot of coolant to lose with no visible leak. You'd be trailing a plume of steam and I wouldn't think it would run so well with coolant getting sucked into the cylinder. Any green dripping out the tailpipe? There were a couple of lines on the underside of the intake manifold that circulate coolant in the throat of the throttle body to warm up the intake air on the 4ZE engine. Maybe the 4ZD is similar? Coolant also circulated in the intake manifold.
Maybe pull the wheel and drop the mud flap to get a better look at the passenger side of the engine. Gurgling is just air redistributing. You don't want to run your vehicle with air trapped in the head 'cause that restricts the coolant from really circulating which will eventually melt the valve seats out of the head... ask me how I know...