Update: Looks like Kandarz updated Everyquest to include this functionality natively, so this addon is no longer needed.
This addon takes the list of completed quests from WoW on the PTR and adds them to EveryQuest as completed.
Note that this only works on the PTR right now. New PTR builds are likely to break this addon until I can adjust for what changes may happen to the API. This only works for EveryQuest, but I'm sure it can be adapted to other quest mods.
If you want to update the list of quests you have completed on Live, you will need to install the PTR, copy your character over, install this addon and Everyquest, use this addon, and then copy the EveryQuest.lua in your character's saved variables back over to live. I'd suggest backing up the data, though, in case something goes horribly wrong.
Due to some quests being listed as completed that do not show up in Everyquest (for various reasons), you can have CQ print out a list of failures. I'd suggest using WoWHead to look these up and see if EQ already has them as completed. I noticed there are some special quests which show up as different quest IDs according to EQ and Blizzard. No idea why.
Again, this is PTR only. Once 3.3 hits, this should work with it.
Note: Low ID quests are showing up for some people in a different data format. I've adjusted this to handle that, but it's possible there are problems with the way I'm interpreting the data or Blizzard is presenting it.