I hope you dust any cuts with a fungicide or at least cinnamon. You are needing to place this plant in an environment that can induce fungus, so be sure you are preparing for this. Also, I agree - if you have three roots, I would plant it. Even if they are small, the constant, even moisture of the planting mix will 'pull' the roots out and aid them in getting started. Be sure you sterilize your mix before you plant. I always just microwave a bowl of the damp mixture for about 3-4 minutes then let it cool to room temp.
You might also look into a transplanting fert., something with B1 or B2 in it; I use a brand called Super Thrive and it seems to really help with aiding in transplant stress; I soak the plants in a solution of it, with a fungicide added (I use Captan), for about 10 minutes. I also use some of the solution to dampen my soil mix so the roots have access to the fert longer and mold does not get started.
As your plant has already experienced root rot, I would be careful with the watering. The first 20 - 30 days or so, I would mist it regularly and often, rather than water it. Until the roots become fully active in their growth, water will only rot them.
Best of luck - Keep us updated!
Steve