A word on snaking.
In many cases, what looks like schedule 40 (heavy duty) drain plumbing may be a thin-wall replica. I know this, because the drain pipe connecting my grey tank to the main dump is made of this thin-wall stuff. While the plastic is fairly durable, don't get too rambunctious with that snake.
It also seems reasonable to point out that a "blocked" vent is not likely to prevent draining altogether. Instead, water will drain and gurgle as air bubbles make their way up through the water as it drains. By all means, check and clean your vents (the "instavent" under the sink and the main vent from the grey tank through the roof. But no draining whatsoever suggests a clogged drain pipe. If you have the P-trap (or J-trap) off, you should be able to run a snake through the pipe.
BTW, if the main grey tank vent is clogged, the question is clogged with what? Could be a nest of some kind...perhaps yellow jackets.

Take your time if you decide to snake the main vent.
One more word of caution. Get out your tape measure and do a crude measurement of the overall length between your starting point and where the grey tank is. Mark off that length with a wrap of masking tape on the snake. This way you know both when to stop and that you "got there" without having the business end of that snake, perhaps, tracing its way all the way down to the dump gate valve or curling up in the grey tank...and possibly damaging something. The ends of snakes are generally kind of sharp.
Lastly, my snake can be driven with a drill, and it has a lever to engage the snake spiral and move it forward or back. This is handy for making 90 degree turns and such. But be gentle with the power. Like I said, you may very well have thin-wall pipe, and these snakes are designed for schedule 40 or better plumbing.