Correct me if I'm wrong and feel free to continue what I was doing lol.
Just did the first 3 teams on the list cause I was getting bored, but Carolina played less regular season games against playoff teams than all 3 of them (16 Pens, 15 Hawks and 14 Kings)
Part of the problem there is, as I mentioned earlier, that season the schedule was incredibly heavy on intradivisional play. The NHL schedule that season for each team was 32 games against your own division (8 games against each division member), 40 games against the rest of your conference (4 games against each of the other teams in your conference), and then 10 games against the other conference (one game against each member of two opposite conference divisions - that year the Southeast played the Central and Pacific, the Atlantic played the Central and Northwest, while the Northeast played the Northwest and Pacific). With only one other playoff team coming out of the Southeast that year and one of our cross-Conference series against the Central Division (which also only had two playoff teams in it) that's a heavy penalty. But that said, here's their record against the other playoff teams that year.
vs. Ottawa - 2-2-0
vs. New Jersey - 2-1-1
vs. Buffalo - 3-1-0
vs. Philadelphia - 2-0-2
vs. New York Rangers - 3-1-0
vs. Montreal - 4-0-0
vs. Tampa Bay - 3-3-2
vs. Detroit - 1-0-0
vs. Dallas - 0-0-1
vs. Nashville - 1-0-0
vs. San Jose - 0-1-0
vs. Anaheim - 1-0-0
That's good enough to earn a 22-9-6 record and 50 of their 112 points earned against other teams that made the playoffs.
That scheduling would be altered in the 2008-2009 season to 24 games against your division, 40 games against the rest of the conference, 15 games against the other conference, and 3 wildcard games and then altered again in 2013-14 to the present format.