You could have him be the version of the Doctor (identical in personality and experiences to the one from Voyager up until 2374) that was in the Kyrian Museum for 700+ years before finally leaving to trace Voyager's journey home to Earth in a shuttlecraft sometime many years after 3074 in the episode VOY: Living Witness.
https://memory-alpha.fandom.com/wiki/Living_Witness_(episode)
Since he had already surpassed the year of The Burn in 3069 and has a long journey ahead of him by shuttlecraft, he could be arriving just in time to be a part of the new Voyager-J crew in 3189, and perhaps even be responsible for its namesake, as a means of reclaiming the good name of Voyager after he had spent so much time and effort in the Kyrian Museum correcting the record. He could also have brought renewed interest in Voyager to future Starfleet's attention.
Along his journey he might have settled down in a few places and required an aging program to blend in, which explains his change in appearance.
https://memory-alpha.fandom.com/wiki/Living_Witness_(episode)
Since he had already surpassed the year of The Burn in 3069 and has a long journey ahead of him by shuttlecraft, he could be arriving just in time to be a part of the new Voyager-J crew in 3189, and perhaps even be responsible for its namesake, as a means of reclaiming the good name of Voyager after he had spent so much time and effort in the Kyrian Museum correcting the record. He could also have brought renewed interest in Voyager to future Starfleet's attention.
Along his journey he might have settled down in a few places and required an aging program to blend in, which explains his change in appearance.