I want to make an observation and I don't mean to scold.
What you're seeing today has probably occurred in the past. Pre-shot numbers do not tell you much about how low a dose of insulin takes your cat's blood glucose numbers. Binnie is getting a substantial dose of insulin.. If you have been (or the vet has been) making dose adjustments based on the pre-shot numbers, especially with increases of 1.0u, it is very risky. Lantus dosing (well, all insulin dosing) is based on how low the dose takes the numbers. As a result, you need to get spot checks so you know how low numbers are dropping. I'm really glad your got that +4 test.
Most cat's nadir (low point in the cycle) on Lantus is somewhere between +4 and +8. However, this is not always the case and nadirs can and do move around. For example, my cat had an early nadir. Her low point was typically around +3, except when it wasn't.
Since you've decided to follow SLGS, you will want to reduce Binnie's dose to 4.75u.
I'm also linking a post from the Lantus board on
how to manage low numbers. It's helpful to bookmark or print out the instructions so you don't have to go digging for the information.
I'd also like to suggest that you consider posting on the
Lantus board. There's a great deal of information and expertise there and everyone is using the same type of insulin.