AFAIK (and I will look for a link) Mexico will not extradite to any place with the death penalty unless it is off the table. I don't think the charges would have to be downgraded, because LWOP would be an acceptable alternative for murder 1. JMO
ETA: Here is a quote and a link to the most comprehensive information about extradition I have found. It's been very helpful in understanding the situation with Brenda Delgado, who is a dual citizen and as such, can only be extradited. As the quote explains, we can hope that Mexico will just deport the Reed creeps, since they are U.S. citizens. If Mexico deports, the death penalty does not have to be off the table and it's a much faster process.
Alternatives to an *extradition
Deportations
A deportation is the fastest way to get a fugitive back from Mexico. The fugitive cannot be a Mexican citizen, however, because Mexico will not deport one of its citizens. Also, when a deportation occurs, there are no political strings attached. For example, to get a capital murder suspect extradited, assurances have to be given to Mexico that the death penalty will not be applied to the case. This is not necessary in a deportation. Another benefit might be getting around the specialty rule, which states that a fugitive can be tried only for the offense for which he was extradited. There are exceptions, but basically the rule is not a concern in a deportation.
Once the Mexican authorities decide (more often than not, they are convinced through on-the-fly negotiations with U.S. agents working the case) to deport someone, it can take between two and six hours before the paperwork is complete. Once that occurs, U.S. law enforcement officers want no further delays in getting their hands on the suspect. This is where our city’s proximity to the border can be an asset—no flight arrangements have to be made. In two recent murder cases the deportation out of Ciudad Juarez culminated with Mexican authorities taking the suspects to one of the international bridges in downtown El Paso and literally turning him loose on their side of the bridge while U.S. law enforcement officers waited anxiously a few yards away on the U.S. side.
http://www.tdcaa.com/journal/update-pursuit-fugitives-who-flee-mexico