Well I may have a solution! The same has happened to my guild and sadly it prevented us from killing heroic Deathwing. I would feel just awful if I didn't get this angry dragon down before the dawn of Mists of Pandaria and I'm actively searching for a guild currently working on H DW or who has DW on farm.
If your guild can't fill a healer spot every week please consider getting in touch with me, as I would be more than able to show for every raid. I have extensive 6/8 experience and some attempts on spine before people simply lost interest. I take time to study fights and come prepared to every raid, and believe I follow mechanics well and play well with others. I can provide my availability when/if you message me.
I'm not asking for a permanent raid spot or even a guild invite. All I'm saying is if you need a bandaid to keep your raid going through the rest of this xpac please message me so we can punch that dragon in the face together!