Well... huh, more confusion.

Here's my latest macro:

/run AcceptGroup();ConfirmSummon();AcceptQuest(); AcceptTrade();RetrieveCorpse();RepopMe();
/click LFDRoleCheckPopupAcceptButton;
/click LFDDungeonReadyDialogEnterDungeonButton;
/in 1 /run StaticPopup_Hide("PARTY_INVITE");

I invited this toon, clicked the macro, and it worked like a charm! I thought great, problem solved, right?

Then I left party and tried it again, just to make sure.... insta-decline - the popup didn't even show up.

After trying this multiple times, when I log into the game the first time it works great, but all other times no matter who invites him until I relog my toon auto-declines. Good grief, I didn't figure an accept macro could be so complex.