How long will it take on average to get my identity verified?
It depends. Some had it in few days, some complains it takes weeks (e.g. when I was verifying my account with coinbase few years back it was in two days).
AFAIK there was huge inflow of new customers lat weeks and lot of exchanges closed registrations for while .. so I guess they will be overloaded.
check cex.io, coinbase.com, kraken.com or bitstamp.net
But I recommend you to try the localbitcoins ... if you find relevant buyer with same bank you can sell coins within few hours (doublecheck user feedbak before making deal).