I am by no means an expert, but in my own experience with the Anabolic Diet:
Yea, there's no way you're not going to be losing muscle mass.
Barbell complexes are a great way to condition, but in my opinion, it won't replace lifting, which plays a large role in helping you retain muscle mass when you're cutting weight.
IIRC, the concern of "doing too much cardio" on a ketosis diet comes from the fact that HIIT uses the same energy pathways as heavy lifting (which is essentially a type of interval training), in that they both tap into your stored glycogen.
In that respect, I would say you're right on the border. I lift every other day on the Anabolic diet, but I limit my HIIT to once or twice a week with an additional hour total of SS incline walking each week.
If you're losing more than 1-2 pounds a week AFTER THE FIRST 7-10 DAYS of switching to a keto diet (where preliminary water and glycogen loss occurs), then you're probably losing too much weight, and you should increase the Calories that you consume. I would suggest that you start closer to 3000 Calories/day and slowly taper them down.
Injuries suck, but the worst thing that you can do is panic. I would strongly suggest creating a post in the Injuries and Rehab forum if you have not already to see if you can get any advice on what you can do besides way too much cardio in terms of continuing your training.