If the balance transfer fee is 3% the convenience check will end up costing you $180.

I'd use your emergency cash to keep from paying that fee. You can always buy $1,000 Visa gift cards for example, use them to load up a Bluebird account, then transfer from your Bluebird to your bank account to replenish your emergency cash.

However, you have to take the APR into account because the amount you pay in interest may outweigh the amount saved by doing the above.