@andyg – here’s another idea, why don’t you see if your clinic can lend you a CGM for a week, so you can have your BG checked for you every five minutes (or whatever frequency they check at) all through the night. You can then see if there are any patterns to what’s happening.
I used to split my lantus, but don’t anymore – just 39 units in at about 7.30pm. I find that lantus tends to peak after an hour or so and then, for me, tail off at about 22 hours or so.