Laura,
I agree with the various suggestions made - all good stuff, especially trying other bullets to find the model the barrel really likes. (There are small but significant differences in 6mm match bullet diameters between the various makes, so it is unusual to find a barrel that shoots everything equally well.)
So far as bullet seating depth / COAL goes, there is a possible issue in 'just touching' the rifling. All makes of bullet see slight variations in bearing section length, shoulder form etc between individual bullets in the box, hence variations in the position of the point on an individual bullet 'ogive' that touches the rifling. Sierra 107 SMKs have a reputation for having a LOT of production variation compared to some other makes. (You can batch them by length using callipers and a Hornady / Stoney-Point or Sinclair bullet comparator tool with a 6mm insert installed to measure the length from the bullet base to the 'ogive'.)
My 107s - old stock packaged in reinforced cardboard cartons - have significant variations in this measurement. The result is that if you set the seater die up to give you a COAL with the bullet 'just touching' with a bullet selected at random, some of your loaded rounds will be engaged well into the rifling, some just kissing as you desire, and a risk of some being marginally 'out', according to the varying shapes of the bullets as you take them out of the carton. Touching + not-touching in an ammunition lot does nothing at all for group size! Also, as you fire your first few hundred rounds, gradual erosion of the rifling 'leade' will make this situation worse if it initially applies at the margin, so a good-shooting load apparently 'goes off' for no obvious reason.
So you want to seat your bullets so that they are all either well 'out', nominally 0.015-.020" with this bullet if used without length sorting; or well 'in', a nominal 0.015" into the 'leade'. As lots of people have said, the 107 SMK is a very forgiving bullet, so going 'out' is probably a safer bet, especially if there is any chance of having to unload a live round in your type of shooting. This often leaves a 'jammed' bullet stuck in the rifling and the chamber / action / lug recesses full of powder grains. Believe me, you want to avoid this as cleaning every last kernel out is an onerous job since they stick like glue to any surface with gun oil on it, even more so bolt-grease!
Another thing to be aware of is that Savage barrels are very well made by mass manufacturing standards, but have a rough internal finish compared to a custom barrelmaker's products. So they usually take quite a lot of 'running in' before they give their best performance compared to a Bartlein, Krieger, Broughton, Pac-Nor etc. Most Savage PT, F, LRPV etc owners see a noticeable reduction in group size at around the 250 round mark.
Have fun, you should get good results with this set-up.
Laurie,
York, England