In my 6 or so years of owning exclusively Tikkas (I own 3, and my friends and family now own a combined 4 more after shooting my guns), all with the original stock modified as others have described (vertical grip, flat fore end, cheek piece, massively free floated barrel channel) and factory trigger with lightweight spring, I have found there are some specific aspects of my shooting form that really improved my accuracy with the guns.
To be clear, I don't think these are necessarily specific to Tikkas, but I think they are recoil control tips applicable to any lightweight gun (which Tikkas are, noticeably lighter than MOST guns) shooting a medium to high recoiling cartridge (which most hunting rifles are, and most Tikka chamberings are).
First, I've found much better results giving the gun more shoulder pressure, ie preloading the rifle into my shoulder and making sure that the contact patch on my chest is uniform and firm (no gaps, angles, jacket edges, straps, etc). This helps reduce muzzle jump and overall gun deflection, and improves groups. And really, your whole recoil management "chain" needs to be carefully set for each shot, ie shoulders square, base (whether seated or prone) square to the gun, rest is firm and gun tracks straight back and forth. All of this helps to reduce and control the gun movement under recoil.
Second, I have actually gone the way of INCREASING my trigger weight from the minimum setting with the light spring. I'm talking a turn or two in from all the way out, which probably gets closer to the factory spring at it's lightest setting (but I still prefer the lightweight spring for overall trigger feel). I think there is such a thing as a trigger that is too light for a given amount of recoil, because at a light setting, when the gun goes off, there isn't enough force on your trigger finger to ensure proper follow through and keeping the finger on the trigger all the way through the shot. I think if you have good trigger pulling mechanics, a slightly heavier trigger shouldn't cause accuracy issues, and can help with follow through. Lots of dry fire practice will tell you if your trigger pull is correct or not. The crosshairs SHOULD NOT MOVE, not one bit, through the trigger pull.
And finally is the cheek weld/scope height/eye relief geometry. I think high recoiling rifles expose flaws in this ergonomic combination and getting a comfortable and repeatable head position from multiple shooting positions also means you get your upper body in a comfortable and strong position. If you are hunched or craning your neck at all to get your eye on the scope, your posture is weaker and your recoil management will be worse. I have personally settled on a cheek piece with roughly 0.25" rise and some negative cant (which mimics the factory Tikka Varmint stock cheekpiece), and medium height Talley lightweight rings (1.9" scope height over bore). I am a tall guy, and this combination helps me keep my head and neck in a more natural position, and helps me keep a good open/strong chest and back posture whether standing, seated, or prone.
