Your correspondent E. D. might have gone much farther back for an example of the use of the word party for a particular person. In the Tempest, Act III. Sc. 2., we have:
"Cal. I say by sorcery he got this isle.
From me he got it. If thy greatness will
Revenge it on him—for, I know, thou dar'st;
But this thing dare not.
Ste. That's most certain.
Cal. Thou shalt be lord of it, and I'll serve thee.
Ste. How now shall this be compass'd? Canst thou bring me to the party."
Erica.
Warwick.