There are multiple reasons why you should cross-train when preparing for Obstacle Course Racing. Three reasons are: Typically it will lower your risk for injury, it gives you variety in your training to keep things from becoming monotonous, and it will help you improve areas of weakness to become a better athlete overall.
We'll keep this quick and easy, because I know you need to get back to training. Below we've listed cross-training options that are most applicable, and have the most carry-over for OCR.
Cardio Training Options: Cycling & Cross-country Skiing/Skimo. Both require a lot of work from your lower body, but without the impact that running delivers. I've personally been working on cycling more as cross-training for my running, and to help develop more strength and endurance specifically in my quads. It's been great! Either of these options are fantastic. Of course, you could also use a Rower or Skierg. You could swim, or you could hop on an Airbike. However, those training movements will have far less carry-over to your OCR performance. Feel free to do them, but Cycling and Skiing are going to be my top suggestions BY FAR.
Strength Train Upper Body: Yes, the majority of OCR is running, but there are lots of carries and many obstacles which require you to be able to hold your body weight from just your hands. Besides just practicing obstacles, you need to train for obstacle completion by training properly with resistance. My top recommendations for upper body strength training for OCR are Pullups (any variation - bodyweight, weighted, assisted, whatever you can do), and Pushups (again, any variation - bodyweight, incline, decline, weighted, kneeling, plyometric, etc.)
7 Training Days Per Week
The Ultra OCR training program demands dedication and determination. Athletes need to allow at least 12 weeks of training prior to their Ultra. Each week, you'll have 6 days of training followed by a 7th day of fully programmed recovery work. If you're ready for the challenge, sign up now.
Strength Train Lower Body: You should also be implementing lower body strength training exercises. Training this will allow more power and strength of movement, as well as decrease your risk for injury by (you guessed it) strengthening your lower body. My top 2 picks for lower body strength training are Weighted Lunges and Weighted Step-Ups. Both require a single leg to do the majority of the work and both simultaneously develop greater stability in your ankles, knees, and hips which is essential for runners.
You'll be hard-pressed to find an athlete who does the exercises suggested above regularly/competently and doesn't do well at an OCR.