As an Oilers fan myself I also landed on Dallas as the last team we had trouble scoring on in the playoffs, however I can't really remember if it was due to goaltending performance or just team defense/the defensemen Dallas had.
They were just a really good team. Modano, Hatcher, roaming goalies, Zubov, Hull, Nieuwendyk on the cup winning team in 98. Team was built for the DPE... went to back to back cups in the late 90s and were still solid up to 04, but I don't think they see that level of success outside of that era. Ran into those HOF Avs and Wings teams in the early 00s, probably why they didnt see more finals.
Honestly those three teams owned the west for a solid decade (wings even longer). But Dallas was the most frustrating of the three IMO, never opened up. Every game seemed like a slog. I remember jumping like a psycho when Marchant torched them in 97 OT (funny), down the right side, cut across, series over.... I was six LOL. Kovalchuk would go on to do that for years, but I'll always remember that goal. They went on to back to back cups the seasons after that. Eerily similar to Detroit when we bounced them in 06.
Edit - it's interesting how fickle the goalie positions is. Sure Dallas mostly played good team D, but ITT most of the suggestions are average goalies, catching lightning or something. Other worldly nonsense that sticks with you. Id expect more about Roy, Hasek, price, Lunqvist, Luongo, etc. Maybe we expect them to step up more often and steal games, so it's less heartbreaking when it happens. But when Halak, Guiguere, roloson, Kipper, cujo, etc put up like 1.4GAA in a series people are rattled forever. It's not even that Turco and Belfour annoyed me because they played unreal, they just pissed me off because everytime we entered the zone they cover up for a faceoff we couldnt win against Modano, or every dump in went back off the glass and out.