When I used a LOVE control in similar set-up to what you describe I generally got no more than 1 or 2 degrees of fluctuation in temp with it set to a 1 degree band.
Is the HEX swinging 4 degrees or is the mash swinging 4 degrees? How fast are you flowing the wort through the HEX?
I found that I get better accuracy if I dough in and slowly open the valve controlling the recirc to wide open. If I tried to throttle it down to a flow like I would use during a sparge, I got wild temp swings like you describe.
In this pic you can see I have the love is reading 99 degrees. I have it set to 100. The 2nd thermometer is reading 99.2 at the bottom of my mash.
This system worked very well for me.