Despite that sinking feeling in the pit of my stomach, I'm going to try and summon some optimism in the midst of looking at other non-Nathan options. The option in question here is a therapy called platelet-rich plasma, and there is a precedent for using it to heal an injury very similar to Nathan's. I'm not saying this is in any way likely to happen, but in the face of potentially career-ending Tommy John surgery (Nathan is 35) I have to believe that the Twins will at least take a look at this.
In July of 2008, Takashi Saito, then closer for the Dodgers, sustained a 50% tear of his UCL (I haven't seen a percentage for Nathan, but Gardenhire described it as "significant"). As detailed in this LA Times article, Saito, then 38, opted to go with an injection of platelet-rich plasma rather than surgery. Despite its use in other sports, notably in helping Hines Ward and Troy Polamalu recover from injuries during the 2008-2009 NFL season, PRP injections had never been tried before on a pitcher. The procedure involves taking the athlete's own blood, placing it in a centrifuge, separating the red blood cells from the platelets, and injecting the platelets at the injury site. Although some of the major publications in the field, such as the Journal of the American Academy of Orthopaedic Surgeons, have said that there isn't yet clinical evidence that the treatment is effective (and the doctor that performed Saito's procedure also said he couldn't be sure that the PRP was the definitive reason for his recovery), the fact remains that Saito was back on the mound for the Dodgers in October of the same year. Given, it wasn't the ideal appearance as he gave up 2 runs on three hits without recording an out, but he managed to have a very respectable (and injury-free) season with the Red Sox last year, posting a 2.43 ERA, a 1.35 WHIP and a 52/25 K/BB ratio in 55 2/3 innings.
Do I think there's any reason to believe that the Twins and Nathan will use this option? No. But it's out there, it seems to be very low risk, and there's a chance it could aid the healing process without surgery. I hope they'll explore it further, but I'm not holding my breath that we'll see Nathan pitch this season.