Hi, I've been struggling with exactly the same issue, I always went higher in the late hours of my Lantus shot (after dinner).
However, after doing some basal tests I actually found out it wasn't the Lantus at all! I was having a prolonged spike from dinner which always contains more fat than my other meals...
I noticed this when I tried to skip dinner once, my BG was absolutely fine!
If I were you I would definitely test this first, if not then obviously you will need to split doses and I would go for Levemir and then split or even go for an insulin pump.
Hope this helps you