Update: I've encountered and solved a secondary issue of 360 video editing in Vegas. 360 video has an inherent attribute of being a 2:1 aspect ratio (apparently), and thus does not by default work properly in Vegas if the timeline is not also set to a 2:1 aspect. Importing 360 video into a 16:9 timeline for example will result in a black hole at the poles of the video due to the letterboxing caused by squeezing the wider 2:1 footage into a 16:9 frame. This is a problem if you want to output a video composed of both 360 and standard 16:9 (or any other aspect besides 2:1) camera footage.

Fixing this is rather simple. Just right click the footage, navigate to properties, and uncheck 'maintain aspect ratio'. The footage will now display properly and cause no issues when rendering out to a 16:9 format. Vegas's project properties should be set to the nearest possible resolution as the 360 footage, but at the desired aspect ratio as the final output. My camera for example outputs 5.7k 2:1 footage, so my timeline is set to 5k 16:9. From there I can render in 1080p, 4k, or any other resolution at 16:9 aspect.

A script for disabling 'maintain aspect ratio' for all clips can be entered into a notepad file and saved as a .cs in the Vegas/Script Menu folder (thanks to skorch82 for this script, which I only had to modify the paths of to get working properly with the Magix version of Vegas http://forum.gameanyone.com/index.php?topic=6773.0;wap2):

using System;
using ScriptPortal.Vegas;

class EntryPoint
{
    public void FromVegas(Vegas vegas)
    {
    // get the tracks in the project
    foreach (Track track in vegas.Project.Tracks)
    {
         // if the track is video, then you can set the event
         if ( track.IsVideo() ) {
              // get all the events on the track
              foreach ( VideoEvent vEvent in track.Events ) {
                  // uncheck maintain aspect ratio
                  vEvent.MaintainAspectRatio = false;
              }
         }
      }
   }
}