First of all, your cat didn't become diabetic overnight and he's not going to be cured overnight either. It was a good 5-6 months before I started to see some kind of pattern with China so take it easy on yourself!!
Next, you started at a VERY high dose! Most cats should start at .5 to 1 unit twice a day. Starting at 3 units is pretty insane (but it seems like a lot of vets are certifiable! Mine told me to start at 4U but he was sure she'd need much more....she never needed more than 2.75)
If Frank were my cat, I'd reduce the dose down to no more than 1 unit...Seriously!! Continue getting a couple of tests on the AM cycle between the shots and always get at least a "before bed" test on the PM cycle. Most cats go lower at night so it's really important to get at least 1 test before you go to sleep at night.
I don't know if your vet is guiding you on dosing or if you're grasping at straws and just trying to increase to see something work, but too much insulin can cause your cat to be in a constant fight for their life. If the dose is taking him too low, the liver will release stored sugars and hormones to bring him back up. It can take up to 6 cycles for those hormones to clear the body so increasing the insulin just gets him stuck in a cycle of driving him too low, liver dumps hormones, glucose goes high again, etc. etc. etc.
Please try giving just 1 unit for the next 3 days and let's see what happens. We had a cat come to us on 25 units....when we convinced the caretaker to reduce down to 5, the numbers remained high...so we reduced again....and again....ended up, her cat was in remission for no telling how long but because the numbers were always high (due to that liver dump) she just kept increasing it.