In fact, upon further recollection, Rick Sternbach was busy designing Voyager and really didn't have any real input on the Enterprise-E.
I'm not sure that the timing of that matches up? Voyager had already been on the air for a couple of years by the time Star Trek: First Contact came out.
This says the design process started in the fall of 1995.
http://www.starshipdatalink.net/art/1701-e.html
Voyager premiered early in 1995.