Extremely hazy hefeweizen

Hi, I´ve brewed a 5 gals Hefeweizen batch 10 days ago with some troubles when recirculating. It was a 10 # pilsen and 10 # wheat malt very simple. The point is at the moment I was trying to recirculate this wort I realized that I had forgotten to loose a bit the mill crushing gap to get coarser grinding (because of the wheat) and the consecuences were there to punch me in the face... the famous stuck grain bed. After doing many tricks to solve the problem I gave up and stirred the grain bed to start fly sparging. Result was I had collected 7 gals of a extremely hazy wort ending up with a 5,5 gals to be fermented. Fermentation has been done , beer is aging in a fridge at 40 F. Beer color looks like a milky-buttery liquor , it tastes very good,nice wheaty tones and clove, no astringency yet. My concern is there must be a ton of proteins dissolved so I think its shelf life could be very short. Do you think I should use finings before bottling-kegging to extend its shelf life?. Should I let it go as it is to do not lose this nice flavor?. It´s the first time in years that I brew a beer without a proper recirculating, I don´t know the aftermaths of doing this. TIA