Update:
Looks like it works on part of the message header, but not the part that seems to matter. These look good:
X-eSCM-MailFrom: <jdoe@example.com>
.
.
.
Return-Path:
jdoe@example.com
But PostFix doesn't change this one, and it appears to take precedence:
From: "John Doe" <jdoe@exchange.example.com>
X-MimeOLE: Produced By Microsoft Exchange V6.5
Can that address be changed via PostFix on a relay server? Any insight is greatly appreciated.