4. The answer is 4 years.
Putting aside the fact that I was joking, I didn't say it was 400 years I said it seemed like 400 years. And in all seriousness by the end of the 90's the cup seemed like a few lifetimes ago. The 97-98 season alone felt horrifically long.
Since 1996-97, the Rangers have had 5137 man-games played by left handed shooting defensemen, and 2738 by right-handed shooting defensemen. So their current 4 LHD/2 RHD layout is pretty consistent.
The Rangers started the season carrying at least 3 righty D in '90-'91, '91-'92, '92-'93, '93-'94, '94-'95, '95-'96, '96-'97, '97-'98, '06-'07, '07-'08, '08-'09, '09-'10, '10-'11, '11-'12, and '12-'13.
15 out of 23 seasons.
Every year they've made the playoffs since '91 they've had 3 righty D's, except the year after the '04 lockout.
Every year they missed the playoffs they've had less, except the year before the cup, '97-'98 and '09-'10.
Playoffs with 3 RD = 12/15
Playoffs with less than 3 RD = 1/8
Pretty much every year the Rangers had some semblance of a properly constructed team (i.e. not the end of Smith/beginning of Sather's tenures where they just seemed to throw crap at a wall to see what sticks) they've tried to roll with 3 and 3.
Considering that some teams roll with all lefties and most with less than 3, I don't think its a stretch to say the Rangers put more stock in it than most teams.