That's an interesting section to choose, but good riding and at a fairly good time of year.
(I don't remember much of this section, except bonking while heading south up the hill to Pinos Altos, because I counted on a country store being open on during the pandemic.)
I will say - unless you've already partaken don't forget to figure out how to have dinner at the Buckhorn Saloon and Opera House in Pinos Altos. Top notch chef and a surprising menu and a good way to celebrate the climb up from Silver City. I think they're open mon. - Sat. at 3 PM with food at 4 PM. Perhaps a late start and a shorter day to shake down, with camping in one of many prime spots in the Gila.)
The fire season starts early down there. Agree (as always) with John's advice - the Gila National Forest Service folks might be able to comment on areas of the Gila that have been affected. Their website can also keep you up to date on any active fires at the start of your trip.
In addition, there is also the temporary road closure section of the forum to check closer to the trip:
https://forums.adventurecycling.org/index.php?board=15.640.
You might also double check the maps update section of the ACA website:
https://www.adventurecycling.org/routes-and-maps/adventure-cycling-route-network/map-updates-and-corrections/?routeAddendaaction=mucDisplay:main.results&id=724&mRoute=2&mSection=56#mucResultsThe Tour Divide starts this year on June 9th. The south-north riders should be in Silver City on the 10th. That said, their website - such as it is - might have updates on closures and alternate routes leading up to your trip.