I recently bought the complete Blu-Ray boxsets of both ENT & TOS and I'm currently about a third of the way through season four of the former and I'm actually looking forward to watching 'These are the Voyages'. I think the problem with the episode for most fans is two (possibly three) fold: The holodeck, Trip dying & possibly the choice of episode for the framing story may also be an issue for some. Another way of looking at this episode and I would imagine it was Berman & Braga's, is that of all the past Enterprise captains Riker could have chosen to seek advice from, he chose Archer. Not Pike, not even Kirk, but Archer. In other words it was meant as a compliment. It's my understanding that there is no overt reference to Star Trek: Enterprise in 'Star Trek: Nemesis' and with there not likely to be any other Trek on the horizon at that point in time, they were running out of opportunities to get the 23rd/24th century shows to acknowledge ENT's existence in continuity, so they chose this.
There is also the fact that it flies in the face of what was established vis a vis how much information existed on Starship operations to make such a detailed recreation. In 'The Menagerie Part 1' Mendez remarks that no ship kept records that detailed when he first saw the opening shot from 'The Cage' though this is at least partially disputed by both the previous production episode 'Court Martial' with the (fabricated) recording of Kirk pressing the ion pod jettison switch as well as the flight recorder scene in 'Star Trek III: The Search for Spock'. Because lets face it, if Enterprise's records were that detailed Picard & co wouldn't have gone into their first encounter with the Borg in 'Q-Who' blind. From his examination of the history of prior Enterprises when he was appointed X-O of the Enterprise-D, Riker would have known about the incident depicted in 'Regeneration'.
I want to preface what I'm about to write by saying I'm well aware of the limitations the makers of the show had, and the availability or lack thereof of specific actors & actresses but I've been mulling over alternative ways they could have done a 'These Are The Voyages' type story. Ones marked with an '*' involve using flashbacks instead of the holodeck to tell the ENT portion of the story.
*1. It is 2245 and an elderly Tpol is visiting the USS Enterprise NCC-1701 as its commissioned under the command of Captain Robert April. She and April get talking and she tells him of the NX-01's final mission as an inspiration to April. In a nice nod, in conversation it could be suggested that Enterprise was to have been called 'Yorktown' but for her intervention in honour of Captain Archer who recently died.
*2. I don't think it was established Phlox's age/longevity so this is why I've chosen him for this one. In this story an elderly Phlox could have still been living at the time of TNG and accompanied McCoy as another former Enterprise physician on the USS Hood during 'Encounter at Farpoint' to visit the Enterprise-D. Using a partially recreated sick bay set, body doubles for the elderly McCoy & Data the framing story could have seen Phlox talking with a member of the D's sick bay staff about their facilities - it could have even been Susie Plaxson as Dr. Selar. She did appear in the series in season two as an Andorian - and by way of comparing and contrasting the two ships' medical facilities, he could have told her about the incident that comprises the main story.
*3. This one is closest to the episode as broadcast. It is set aboard the Enterprise-D during the events of 'Pegasus', but instead of the holodeck, Riker is in Ten Forward where Guinan encounters him, asks him what's wrong and Riker tells her about his crisis of conscience. By way of advice she tells him of an encounter she had with Archer and the crew of the NX-01 more than two-centuries earlier. Based on her story, Riker resolves to talk to Picard. The added thing of this is that as I recall Whoopie Goldberg didn't appear as Guinan in season seven so this would be a nice way of retrospectively inserting her into it. It would also be a very 'Guinanesque' thing to do. There is a variation on this story in that it is set during 'Best of Both Worlds Part 2' when Guinan visits Riker in the ready room and concludes with 'And thats now your chair'. The scene could encompass her telling Riker about Archer and how he overcame overwhelming odds.
4. It is night in the captain's quarters aboard the USS Titan. Riker can't sleep due to the ship's current mission and in order to get a good night's sleep, at least for herself, Deanna pushes Riker out of bed with a suggestion to visit the holodeck and seek inspiration from someone who faced a similar situation. Riker's follows his wife's instructions and chooses the NX-01's final mission. Although it uses the holodeck and assuming none of the regular cast perish, it would have at least moved the Star Trek story forward by setting the framing story after 'Nemesis'.
Anyway those are my ideas. Make of them what you will. By the way on the subject of 'Pegasus' was Riker's transporter twin Tom Riker also arrested given that the events of 'Pegasus' predate their splitting in two?