Remove the W DoT and instead while W is up Nautilus auto attacks deal bonus damage equal to his passive on each auto and his autos cause a small knockback but only once every X seconds per enemy.
This whole thing I'm not really fond of for multiple reasons. First, it incintivizes building a certain amount of attack speed on Naut. I shouldn't want to build attack speed on what is probably the most dedicated CC tank in the game. The DoT prevents that from being the ideal option, even though half the damage is dealt up-front on-hit.
The second problem is that by doing this, you're giving him way, way more laning presence, without helping his jungle much. Right now, he has to level the W to get damage from it. Top lane Naut never does that, but Jungle Naut usually does. That means that top lane Naut would be getting a bunch of extra free damage, while jungle Naut isn't getting a significant increase over what it already has.
There's a much easier solution. Give the W bonus damage towards monsters, or just give it a straight damage buff. Right there, the problem is solved, and it doesn't create new issues.
E needs the base value gutted but instead give it bonus damage to monsters and increase the slow and/or the duration of the slow.
I can agree with giving it bonus damage, but why gut the base value? There's no need to do that. He doesn't need to lose the ability to use it for trading. This is just trying to dick over other roles, instead of just making him a better jungler.
Just buff the W, possibly by increasing monster damage. That's all he needs to be a better jungler.