I've been on Toujeo for a while now and i had lot's of problems with night time highs too, still often do. I've started raising the dose but then i had lows during the day. However even with the highs my hba1c actually dropped and after a while making adjustments to my diet too i must say i'm fairly stable.
One thing to keep in mind is that Toujeo clogs up the needle much faster, they advice to regularly change the needle and eject 2-3 units with force before injecting to make sure you're getting your requested dose. It does take a few days to get the full effects from Toujeo and from an increased dose, but right now i think i might prefer Toujeo over Lantus. My day time values are really stable and within a good range, it's just my night/morning that tends to rise but i've always had that even on Lantus. I just wake up earlier now to inject a dose of fast acting to bring me down.