I think the episode could be salvaged, but I would change wide swaths of it, and not make it the finale at all 
If you want to do a TNG-crossover, move it earlier in the season. Make it just a regular episode where Riker and Troi are looking at an historical hologram of the NX Enterprise. I'm not sure you really need to set it during The Pegasus, Riker and Troi were slightly too old to be believable, and the framing device isn't really that important. You can still have Shran appear and request Archer's help with a secret rescue mission, but Trip's death shouldn't happen at all. Honestly, this episode might even be better in the third season rather than the fourth, which was already a bit too heavy handed on the callbacks. It would also fit the theme of "moral dilemma" better if set during the Xindi conflict.
I say either let Terra Prime be the finale (bit of a downer though..) or create a new episode that leaves the series on a high note. Trip and T'Pol bond over the death of their daughter and Archer still gives his big speech. You can have Phlox or Hoshi or someone leave the ship if you want a big goodbye moment. The issue I have with the finale, aside from them killing Trip off for shock value, is that they wanted it to be a goodbye to that era of the franchise, but went way too heavy-handed with it. You don't need Riker and Troi and the Enterprise-D literally on camera waving goodbye, this was a show set during a turbulent era made during turbulent times. Add some nuggets of hope for what we know to be a bright future ahead of them and the rest of the franchise.

If you want to do a TNG-crossover, move it earlier in the season. Make it just a regular episode where Riker and Troi are looking at an historical hologram of the NX Enterprise. I'm not sure you really need to set it during The Pegasus, Riker and Troi were slightly too old to be believable, and the framing device isn't really that important. You can still have Shran appear and request Archer's help with a secret rescue mission, but Trip's death shouldn't happen at all. Honestly, this episode might even be better in the third season rather than the fourth, which was already a bit too heavy handed on the callbacks. It would also fit the theme of "moral dilemma" better if set during the Xindi conflict.
I say either let Terra Prime be the finale (bit of a downer though..) or create a new episode that leaves the series on a high note. Trip and T'Pol bond over the death of their daughter and Archer still gives his big speech. You can have Phlox or Hoshi or someone leave the ship if you want a big goodbye moment. The issue I have with the finale, aside from them killing Trip off for shock value, is that they wanted it to be a goodbye to that era of the franchise, but went way too heavy-handed with it. You don't need Riker and Troi and the Enterprise-D literally on camera waving goodbye, this was a show set during a turbulent era made during turbulent times. Add some nuggets of hope for what we know to be a bright future ahead of them and the rest of the franchise.