OK, here's where I think things took a wrong turn....
When your vet upped the dose from 1u BID to 3u BID. That's an insane increase. It's triple the amount of insulin. The correct adjustment would have been up by .25, or at most .5. What has probably been happening since then is that his system is fighting like hell to offset the insulin every day. His BG will start to drop (and as far as he's concerned, it is falling too quick and too far), and it tries to "self-preserve". His pancreas tells his liver to dump "sugar" into his bloodstream to push his BG up to safe levels.
You may not see this happening. It can be happening between tests, even if you are testing at AMPS and +6. It's all instinctive. Here's a simple "what happens":
Glycogen is the storage form of glucose - think of it as a bunch of glucose molecules stuck together in a form that's too big to escape into the bloodstream.
Glucagon is a hormone produced in the pancreas and it's "job" is to increase blood glucose by triggering the conversion of glycogen back to usable glucose that can enter the bloodstream from the liver. It also stimulates the liver to make "new" glucose from protein sources (gluconeogenesis).
That's from a "think tank" topic that took place 4 years ago.
http://www.felinediabetes.com/phorum5/read.php?15,675616,1196248#msg-1196248
And it doesn't even have to be what we would consider a low number. It's what his body thinks is a low number. Right now, to him, 300s and 400s are "normal". This reaction can happen if he drops into the 200s or lower. As long as the dose is doing "too much", it will continue to happen. At some point, what can happen is that the liver just can't keep up, so there's nothing except for your intervention, if you happen to catch it, to stop his BG from falling to unsafe numbers.
The easy way to avoid this is basically to "start over". Go back to 1 or 1.5u per shot. Test before every shot, and keep the dose the same for a few days. Test at different times between shots. Like one day you can check at +3 and +6, the next day at +4 and +8. Eventually you will have a good picture of what that dose does to his BG. Then you can evaluate the data, ask for advice if you feel it will help, and adjust the dose if needed.
Increasing the dose by 200% is just not a safe way to treat the condition. Jumping 2 units at a time, same thing, not safe. And you can't adjust a dose based on a curve run at the vet's office. First off, you never adjust your dose based on a single 12 hour period. ACtually, from looking at the data, the vet determined to increase the dose based on one seven-hour time period. From 3u to 5u because his cycle that day was not a good one and the 3u didn't drop his BG much. That's crazy. It's just not a big enough sample size to judge how a dose performs. Also, when most cats are at the vet, they are stressed. Unfamiliar noises, smells, people, etc. It raises their BG numbers, sometimes they can be 100 points higher than they would be at home. You have to have days or weeks worth of data to logically make dose adjustments. You have to see what today's dose does for 3 or 4 days to draw any conclusions as to if it is "right" or not, and that conclusion can't just be made looking at preshot test results. Yes, they tell you a snapshot in time of what the BG is. But they don't tell you how high or low the BG was the rest of the day.
Please understand, I sure as hell am not a "know it all". And you are getting advice from a trained professional who you are paying damn good money to. But the way you have described it is just not the way that insulin doses are safely determined. Your vet may be a super fantastic vet and you might feel comfortable with his advice on every condition or illness you have ever needed him to help you with. But as far as feline diabetes, I'm sorry, I don't think he's on target. If nothing else, see if you can find a 2nd opinion for your sake and most importantly for Sonic's sake.
Carl
My tears are not conducive to a calm testing time. Any thoughts are appreciated.
I didn't know about the rice-sock. I'll try it for Sonic's PM shot. Just did a curve yesterday and Sonic is a bit irritated. Perhaps I'll try a paw as well! 
