Is it possible for you to get a test later in the cycle when he sees a lower number like he has been for the last 2 mornings? The idea is to see how low he is going on this dose. Lantus dosing is based on nadirs - how low a dose takes the cat.
For constipation, you could try adding some fibre to his diet like plain, unspice pumpkin or psyllium husk (metamucil - unflavoured). Some folks also use Slippery Elm Bark.
https://www.felineconstipation.org/prevention.html