As Alan says it's a difficult one to answer...
I wouldn't say that people like to split Levimer, it sort of done as being the best option...
You say that when working is the period when you suffer most hypos, I ponder if Levimer is your main problem!
With bacground insulin we are looking to create a flat basal profile, this in many respect is almost impossiable to achieve, so we look to create the flatish possible, sometimes spliting and adjusting timing makes the difference to how flat we can achieve... But we will be left with a certain amount of peaks and troughs to the profile line through out the day...
Having a reasonable idea where these lay within 24 hours is quite important, as these will help determin how best to adjust dose of Quick acting insulin when were are eating/exercising... As you can adjust your carb:insulin ratio to include peaks and troughs.. Same goes for corrections..
It may well be that you are actually injecting too much quick acting insulin on a work day!
As alan says, you need to work out your basal profile, if correctly set then this shouldn't deviate +/- 2mmol/l of your starting point there are a couple of things to remember though about testing as follow;
Only test on rest days, don't attempt to test when doing pysical exercise etc so work day not good idea..
Keep hypo treatment, meter and insulin near to hand
Stop testing if hypo or hyper, treat as appropiate and test on another day..
Once you've got your picture on whats happening with the basal profile, and hopefully sorted you should be able then to work out, what, when and how any carb:insulin ratio, correction changes you need at any point of the day or with particular meals etc etc.