I'm not all that sure about BT's and your case neck...BT's are easier to load in some instances and some rifles just like them, while others like flats...a whole lot of things are going on.
The best way to start reducing group size is to benchrest prep the cases...i.e., weigh sort, turn necks, uniform the primer pocket and bevel the flash hole...THEN do the same with the bullets...weight sort and measure sort the ogives.
Neck grip of 0.001-0.002 is very good, using Redding Bushing dies helps here...adjust your dies to just bump the shoulder of the case...0.001" is all the setback you need.
Vary the seating depth...many 22 cals like around 0.025" "jump" but others like the bullet touching the lands or even into the lands.
Firelapping is a rapid wear process...you're basically wearing off all the burrs and rough machining...high dollar barrel makers us a lead lap, or several as the do wear out...you can do the same with a tight fitting patch using the same grit you pay the high dollars for in the firelapping kits. NEF's have rough barrels so fire lapping or hand lapping will help...just use the finest grit...the object is to polish the bore more than wear it out..
It take conserted effort to get your groups below 1", usually, so read up on on benchrest prepping....6mmBR is a very good website that covers, in depth, just how to go about doing it.
Luck