A friend of mine has had the exact problem you are describing with their 2004 GSXR 600. They have a Yosh Tri-Oval installed with the unswitchable TRE, K&N filter, and the P/C III as well.
We thought the low-end dogging was the stock P/C map so we downloaded the Dynojet recommended map for a Yosh bolt-on exhaust with stock air filter (the closest map to what they had) and the performance was worse!
I talked them into going to a Dynojet certified P/C center (Horsepower Inc) in Erie, PA and it literally did wonders! They strapped it up to the dyno and layed down a custom map for the specific mods that are on the bike. After that was done, there were no hiccups in the throttle response and it was not only more powerful; but more predicable and smooth. Apparently the downloaded map was too rich in the fuel settings (especially down low in the RPMs, below 5k) and they leaned the numbers out considerably in almost the entire map.
I was concerned hearing that maybe it was too much, but they reassured me that they kept the fuel / air ratio within the safe limits throughout the curve in all the gears.
I thought custom maps were all hype until I rode the bike afterwards; then I realized how off those downloadable maps are from the Dynojet website. I think they just don't have enough custom maps to suite everyone's aftermarket configurations.
Hope this helps and you find it's worth the extra $$ to get the custom map done for your bike.