Sweep sometimes times out or otherwise misbehaves…As the bottom of that page says, sometimes it helps to retry and just let it hang for a while.
You can try another way, for example try CoinDaddy’s Counterwallet instance, if the sweep is slow due to slow hardware (Counterwallet.io) maybe CoinDaddy’s wallet will work.
The worst case is you can install Bitcoin Core 0.12.1 addrindex, let it download the blockcain (100 GB or so), install counterparty-server (500 MB download of the database) and then use counterparty-cli to send the tokens to any address you want.
You can also compose the Counterparty “send” transaction manually and sign it, and broadcast it from any Web site or paste it here and someone can broadcast it for you. For this you don’t need to download the addinrdex version of the blockchain, you can use a public Counterparty API server (such as CoinDaddy’s and then you need a bitcoin signing tool to sign the raw transaction…