There is no way a fructosamine test can provide the information that your vet suggested. It's an average for blood glucose levels over a period of 2 - 3 weeks. If you've ever had your blood checked for diabetes, the test is called a hemoglobin A1c. It gives you a single number that is similarly an average of blood glucose over 3 months. It doesn't tell you what time of day your blood glucose is either high or low.
The best way to know if there are variations in Twix's blood glucose is home testing. Like Ale suggested, I think it would be helpful to get some tests during the PM cycle. I'd be very curious if Twix's numbers are dropping at night and you've missed some dose reduction-worthy numbers. Looking at the difference between your AMPS and PMPS suggests that numbers may be dropping at night.
Giving differing amounts of Lantus at each shot time creates problems. Lantus is a depot type of insulin. This is a link to information on the
insulin depot. Ideally, with Lantus, you want to keep a steady level of insulin in "storage." When you give an injection, Lantus forms microcrystals that are deposited in the fat tissue. Much of the insulin dissolves over the 12-hour cycle. However, some is left and overlaps the next cycle. This is what gives Lantus a gentle, "flat" curve. In order to get those results, you want to give the same amount of insulin at AM and PM shot times (unless the dose needs to be changed). If you change the dose at each shot time, the depot never reaches a steady state. As a result, you get wonky numbers.