Could you not just send a transaction of sufficient BTC size to cover the transaction fee (say >=0.015
BTC) into the address and then transfer the whole lot (new amount + dust) out in another transaction to another address for which you have access to the private key?
PROs: you will have the private key for the new address, so can do whatever you want with it... ie. store offline, import into another wallet etc
CONs: you will need to pay two transaction fees to get the money into and then out of the Multibit wallet
Alternatively, you could always just start adding money to the address(es) until their balances become big enough to get them out economically. Maybe get a friend who wants to cash some coins out of somewhere (gambling/faucet/exchange account etc) to pass them through your account, picking up your tagged coins on the way.
I guess it all depends on how much value you place on these coins... if you want them badly enough, you'll cough up the ~0.0002
BTC in transaction fees to get them out...