One option is to have your HLT setpoint higher by ~5-10F of your mash set point and then use MLT probe to turn on and off your pump. This is similar to steam injection on commercial setups.
I had a similar problem with my setup, not 10F but closer to 5F.
My mlt is a 10 gal kettle with reflectix or whatever it's called. Recirculation rate and mlt mixing accounted for some, but not all. Controlling on HERMS outputs caused bulk mash temp to be low by about 5F. Controlling on HLT...