lindy2 . . . . .
There is a popular solution to the resizing of belted calibers that you described. At this time, there are well over 6,000 shooters using the Belted Magnum Collet Resizing Die.

Unlike any FL or NK die, this patented collet resizing die only squeezes brass inward, and not also rearward over the web. You just need to reduce case diameter .001" smaller than one of your FIRED cases.

Measure the diameter of your cases (just above the belt) with the wide part of your calipers, and you will see why your resized cases don't fit. Search for Belted Magnum Collet Resizing Die on Google.

So.... reading through all of this... there is no mention of lubing the neck of of your hull...
Although for the 2 of the 7mm RM that I have - a 1963 M700 (I have the receipt from when my grandfather bought it new), and a 1997 M700 LSS (my wife bought me new for an anniversary gift) - between the 2 all I have to do is a neck size... stuff it in the die with the right "cam over", rotate 90*, hit the "cam over" again, pop a primer in it and we're ready for powder and a bullet... BUT, my neck sizer dies are LEE...
When I work up loads for others, (my FL dies are RCBS, Herters, and Lee) I notice that running the FL dies, I set for the "cam over" on the press - normally in my Rock Chucker, and unless I do a neck lube, the sizing ball seems to stretch the shoulder on extraction without the neck lube... especially noticeable on the Lee dies, as the expander ball will sometimes actually pull out of/ move within the collet on the FL die... this scenario seems to make a hard/ non chambering round...
The worst I've had to deal with FL sizing is the .300 win mag, more so with RCBS than other brands, but it was more over stuck cases (fortunately I have the stuck case remover set)...
IMHO, unless you are stuffing rounds in an auto-loader (ie AR platform, etc.), there is no need to FL size a round on a firearm you own...