Hi Hazel
Both OH and I have been following the BSD (now on maintenance, but following the same principles with higher calorie targets).
I am not Type 2 and wanted to lose some weight, successfully losing over 20 lbs moving from 10 stone 8 lbs to 8 stone 10 lbs in just over the 8 weeks.  OH wanted to get off Metformin, and followed the BSD though on more calories as he didn’t need to lose so much weight, but needed to change his shape and lose the visceral fat.  He has now been able to stop using Metformin, and has had his doctor’s approval for this.
So I focused on 800 calories but in light of comparatively little weight loss to achieve, used this site:
http://keto-calculator.ankerl.com
together with
MyFitnessPal app 
to log on all my food – if you insert your details into the keto site, it will show you how many carbs/protein and fat proportionally you should try eating and you can then set your targets on MyFitnessPal.
OH followed the same principle.
Whilst the carbs on the BSD are good ones, you can experiment with eating less of them.  Because of my target, I set my carbs at 20g per day.  Many people here try 50g or less of carbs, and find the weight loss is very effective.  It can also really help with BS readings.
We are eating real food, not protein shakes.  It is possible to keep the carbs at under 50g eating real food.
I hope this helps you.  I would really recommend trying slightly less carbs for you – I am sure more people on the forum will join in on this thread to agree 🙂