Basically if you believe that you have the player beat and that he will call I would shove, otherwise I would just let him donk off some more money. Since you have 84% chance of winning, the ideal is to get as much from him as possible. If you believe he has an ace or draw at this point, you just need to estimate the likelihood that he is going to call.
There are downsides to shoving at this point, the biggest of course is that he has a full house, and you come up empty. The other is that he lays down a hand that you beat. Another is that he is bluffing and willing to keep bluffing.
Just because the player is loose and aggressive, it does not mean he will not lay down a hand. I would seriously consider that letting him stay the aggressor just might be the best play. Check raising the river all in might work a little better if he has a hand or is on a bluff. If he is bluffing you really have not lost anything because he is not going to call an all in. Better to let him try one more bluff.
If he is not bluffing, just simply believes he has the best hand with some ace and a bad kicker, let him stay in the lead and figure out how to get your whole stack. tipping him off at this point does not help your cause. If you make your move on the river when the pot is something much larger like 6-700 he is more likely to make a bad call, even though he is almost certain you have him beat, since the pot is offering so much overlay.
Some might suggest shutting it down with the all in, may not be so bad, but if you have such a huge edge you do not want him to fold before he has all his money in and concedes at the show down. If you have some bankroll considerations, like your playing with the money for babies milk and new shoes, you might want to try taking the pot as is or minimize what you are getting in.