Since this is a
what-if scenario, afaic the whims of RDM, UPN, and B&B are irrelevant.
Had Equinox been spared, say, if Randy had sacrificed himself for ship and crew? IMO they should have faced an uphill struggle to restore her and Voyager to a semi-spaceworthy* state. Maybe they'd later down the line have to rescue survivors from an alien caravan of refugees at some point, and conveniently some of those could stay to bump the crew count up a little - plus it wouldn't hurt to have some non-Starfleet figures milling about, and drive new character interactions and story opportunities.
As far as personnel transfers, obviously Chuck would be the logical choice to take command; hopefully discarding some of that excess cardboard in the process... Would Equinox's EMH be recoverable and/or salvageable, or would they duplicate Voyager's using a backup module? (if so I imagine 'our' Doctor would ask that his new duplicate be wiped and allowed to begin his own journey of self discovery...) Kim could be a strong contender for transfer and promotion (we got a glimpse of how much more Garrett Wang could do in Timeless, I say give him more of that). I'd let Carey take on Equinox's engines if he were still alive, but I guess Vorik will have to do

I imagine Neelix would prefer to stay on Voyager with the Wildmans, but Chell might be a decent chef for Equinox... And Icheb might ask to transfer, believing he could learn from and offer more to that ship, than Voyager.
*I say "semi-spaceworthy" because I'm someone who feels that Voyager should have shown the wear and tear she was
due after seven years in the DQ. To anyone dismissing that as making the show "too gritty" I ask that you try not to conflate a show's production design and storylines with
characterisation. Trek's characters are largely aspirational; nuBSG's were largely.. not.