You might consider keeping your toon down at the Starfleet Academy and picking up the duty officer missions available there every three days. Those missions pay out in white (and occasionally higher level) duty officers (about eight missions available from four different contacts, with payout of about 11 doffs altogether). The white duty officers are needed for our K13 base development projects (and other projects available on the Armada holdings tab). The occasional refugee doff reward on the missions can be used to get better doffs (most easily on the Asylum on Earth mission which is listed last under the Operations duty officer missions when you beam upstairs to the Earth Spacedock).
You can also do the lore mission available at the academy on a daily basis for 480 dilithium payout (the answers to the lore questions are at
http://sto.gamepedia.com/Lore or in context at
http://sto.gamepedia.com/Accolade/Lore).