Yeah INS doesn't have a stardate so you can be flexible with when it is set. I like to think INS happens after the Dominion War ends. So it doesn't completely undermine how "desperate" the war was as we see and is stated repeatedly on DS9.
By undermine I mean the presentation as it relates to TNG and DS9 during that time period. Maybe the war was a nightmare for Sisko and the gang but for Picard and crew they were probably having a much easier time during the war.
You look at the most notable Dominion War episodes "A Time To Stand, Rocks and Shoals, Sons and Daughters, Behind the Lines, Favor The Bold, Sacrifice of Angels, The Siege of AR-558, Inter Arma Enim Silent Leges, The Changing Face of Evil, and What You Leave Behind" You see the Federation is on the robes quite a lot from the DS9 point of view.
You watch INS and you hear both Picard and Ru'afo talk about the Dominion War as some thing that's in the past. Even Worf who was in many Dominion encounters seems to be more than chipper himself in INS. That's not to suggest the ENT-E had it easy. The sovereign class is a juggernaunt by herself, and we know the Dominion attacked Earth, Betazad, and Vulcan. It's possible they may have led campaigns against other Federation core worlds like Andoria, Tellar, Kronos etc. DS9 was just so damn localized to it's own little niche in the quadrant that any reference to a planet outside Bajor or Cardassia was a very rare occurence. Not to mention other ships fighting the war.
I disagree with you that INS is set after the Dominion War based on several cues (some of which are mentioned by other posters). I would add to the list Picard's comments about Dominion negotiations being ongoing (around "Statistical Probabilities"?), the Federation trying to bring more races in to the fold, presumably to help the war effort (i.e. the Alien race that Picard is meeting with when we first see the Enterprise crew), Picard's comments to Worf about "how they do things on DS9" when Worf fails to show up at his post on time, and the new dress uniforms (which were first seen in DS9 S7 ep "Inter Arnim Enim Silent Leges"- though they may have been introduced earlier but we just didn't see them until then) There is almost nothing to suggest in the movie takes place following the Dominion War. Plus, it was released in 1998, which was the general (real-life) timeframe between S6 & S7 of DS9, making it much more likely for the movie to fall in that time period IMHO