In this hypothetical scenario, it's not practical for me to withdraw directly through any means this exchange provides, so I need to convert it all to bitcoin.
"Hypothetically" the primary reason one would consider not withdrawing fiat is because the account has someone else's name on it. But with Mt. Gox having delays with their withdrawals, it is conceivable someone would want to want to convert to bitcoin, move the funds to another place where they can be cashed-out.
So, the first question... does the exchange support redeemable codes or account-to-account (A2A) transfers of USDs?
Mt. Gox, Crypto X Change, Bitstamp, BtcTree and BTC-E all offer redeemable codes of USDs.
If so, then consider doing a trade by finding a counterparty that wants to move their cash to the exchange that you use. You exchange your redeemable code for your counterparty's cash -- whether it be Dwolla, or Western Union, or whatever.
If redeemable codes are not offered, then you can try another widely used other approach. Generally if you announce the size of your intended order in advance, you might find a counterparty willing to put up an opposing offer at a cross price that works for both of you. You'll occasionally see this with BitFloor or Camp BX where someone has a large order that won't clear without pushing the pice significantly one way or the other. But after pre-announcing that an order would be placed, by the time one is opened there is sufficient interest in unloading a batch of bitcoins for your slightly above spot price.