As glush said, that routing takes you right through the CTR. It's also three miles short of the minimum distance!
Why don't you route past Halfpenny Green? That'll take you well clear of the lower parts of the CTA and they have a working NDB.
For the Gloucester to Leicester leg, you could route via Draycott Water.
Stick your various routes into
SkyDemon Light and experiment that way.
You could ask Birmingham for transits, and they may well give them to you, but in my opinion, messing around with uncertainties on your QXC is not a good plan.