So on the 41st attempt, I finally managed to win the roll for the tier shoulders on my death knight, ending an impressive string of futility. This boosted my average iLvL by an impressive 3 points, by upgrading from my ZA/ZG shoulders and also by allowing me to switch from the tier head piece to the valor head piece.
So I now only need two more pieces of gear on the death knight, both of which can be obtained from the last half of LFR.
I'm debating which character to work on gearing next, but I think I've settled on working on the rogue, since that playstyle seems to match up better with my connection / lag issues. Anything with a long cast time tends to be death for my dps.
Right now, SWTOR is holding my attention from a leveling standpoint, but there is at least a chance I might go back to working on Alliance characters prior to MoP release.