In my own experience, I only got down to the 8% BF area (looking beach ready) through a combination of as much exercise as I could do with as few calories as required to fuel the former. (I uploaded some pix of this journey at my hub). This personally equated to around 2100 kcals a day, mainly low carb (although I am currently leaning out using a higher carb approach and Indigo but it is too early to start recommending this to others).
To put this in context, prior to this, when I first got back into training when I had gained a lot of fat, I employed an HIT programme which recommended x3 full body sessions to failure per week; and a 1600 kcal diet, which was about 50-60% carbs (many of them crappy, as was the entire diet plan). I lost weight but it became hellish and life was always about counting down when I got to eat next. I got lighter and into single digit BF through diet alone as the short sessions burned few calories. However, I also looked terrible and started to resemble a long distance runner rather than weight trainer. People often remarked I looked gaunt and underfed. This eventually led to a re-think and different methods were employed.
Therefore, the upshot, for me, was more frequency and volume, and more calories. Obviously rest and recovery is even more crucial.
Given your injury, you will need to consider a work around if you go down the additional activity route. Someone mentioned KB swings, which sounds like a good plan.
Finally, before I am set upon by the HIT crowd, I appreciate legends like Dorian Yates, Mike Mentzer, etc. got into incredible shape with minimum frequency training and a general balanced diet approach. I’m just pointing out what worked for me.