Sounds good, but now, due to the grouping, I'd try removing the forend tip pressure and see if that eliminates the vertical stringing. I know some guns like it (aparently), but something is causing the stringing - either the tip pressure or the bedding under the lug - perhaps.
Of course, load components, ie: primers and slightly high or low loading can also cause stringing. One merely eliminates the causes, one by one.

I completely floated my 7x57 M600 barrel ahead of the 1" chamber bedding and the .358 Norma and .375 BRNO's 602's behind and ahead of the front recoil lug (devcon bedded) and they all rewarded me with sub inch (mostly 1/2" or less for all) grouping at 100 yards(602's) and meters (7x57) off the bags. The really nice aspect about their grouping, was that a barrel running cold to too hot to handle had absolutely no effect on the grouping capabilities - on any of them.

With the .358 NM I actually beat a 6x47 BR Sporter group for group one afternoon in the 70's I was shooting 250gr. Speers and my largest 5 shot group was just over .250".