Trouble fitting plumbing under new vanity
Not sure how many bends (90's) your drain makes after the vanity, but if only one, you could stick a 90 on the drain coming from the floor of the vanity, and have it sloping up and point towards the back corner of the vanity. You could then run another 90 straight up with an AAV at the top of the pipe and have your trap tie into this vertical pipe significantly lower than the AAV, giving you a long enough pipe after the trap before a vertical drop. This may alleviate the gurgle noise but I do not know for sure. Your trap should be draining into a pipe that has a vent on it, so that when the water does a vertical drop it doesn't cause suction on the trap and pull water from the trap causing gases to escape from the sewer system into your house.