I have a couple of thoughts...
First, and admittedly this is a soapbox issue for me, Somogyi is a concept that is outdated, has not been born out in the research, and doesn't apply to cats who are using a long-acting, depot-type of insulin like Lantus. Michael Somogyi, MD first published an article in 1938 in a not very impressive journal documenting the phenomenon in humans. Subsequent research (on humans) has failed to replicate his results. Needless to say, Lantus and Levemir were not in existence in 1938 so the less than stellar results from the original research can't be generalized to the current generation of insulin. Roomp & Rand recently published a paper that debunked Somogyi in cats using Lantus.
I think what you are describing is what we lovingly (not) refer to as a "bounce." When a cat's numbers drop into a range they are no longer used to, drop fast, or drop low, the liver and pancreas release a stored form of glucose along with counterregulatory hormones and the numbers spike back upwards. While incredibly annoying, this is a normal response. Once Pearl gets used to spending time in lower numbers the bounces will begin to diminish.
When you refer to Pearl's numbers dropping "too low," I'm not sure what you mean. For most of us, too low would be in hypoglycemic territory (i.e., below 50 on a human meter or below 68 on an AlphaTrack). When Pearl drops into the 100s, you're seeing a bounce because she's not used to being in closer to normal numbers.
I also think you've nailed it -- you're not being patient enough. You just increased Pearl's dose. Give the depot several days to stabilize. Depending on which dosing strategy you're using, you give the dose 3 days/6 cycles (Tight Regulation) or a week (SLGS) to settle.
Most of us would feed several small meals each cycle. It's easier for your cat's metabolism and pancreas to accommodate several small meals vs one large meal each cycle.