It looks like Poloniex now only offers 3 tiers. Looks like you are on the old Level 1 (which allowed for $7k daily withdrawal). Level 2 (which requires a picture of Photo ID, a picture of you holding Photo ID, and all sorts of other info) only would get you to $25k daily withdrawal. They have a higher tier (or so they say) which allows for higher withdrawal limits, but you have to contact support at https://poloniex.freshdesk.com/.
To be honest, I would not try to rush getting access to your money as it would be worse for Poloniex to "freeze" things and then require even more info.