I have shot Rem brass forever with fantastic accuracy in my 7 Mags, and have New Win to load when my Rem runs out. Primer pockets do not hold up as well in the Remington, but these are hunting rifles, not target rifles.
I run warm loads in all my 7 Rem mags, and this is where the best accuracy is of 3/8" and smaller groups at 100 yards. Even in new brass, the groups are small, but I am aware that there may be a flyer out of the group, 3/8".
OP, your load is light, and this worries me on fire-forming brass. Fire forming with minimal loads can lead to excessive case stretching. I am not saying that you are getting excessive case stretching with your load, but I would use a 35-caliber ogive gauge on your caliper and measure the headspace length from the base of the case to the shoulder to see if you are getting erratic results.
I hope you take Bob Wright's post to heart, he is spot on.
Tikkas have some long freebore, and this is a good and bad thing. You can run some higher pressures as the long leade drops pressures around 5000 cup, but you will have to up your charge. The standard freebore length in SAAMi spec chambers is .110 which is fairly short, but I can not say what CIP European spec is for the Tikka.
Your 160g should be running around 2950-3050, but every barrel is different.
I run these loads in Remington 700's with 160g:
61g of H4350, work up to this load with Rem 9 1/2 primers in Rem brass
65g of R#22, This is a warm load in Rem and use cci 250 in Rem brass
68g of R#25 with a Winchester Mag primer, work up to this load
71g of Retumbo with a fed 215, work up to this load
Fire forming the new Winchester brass, run it through a neck sizer, put a heavy chamfer on the inside of the case mouth, de-burr the outside, and work up a load. The process used for long-range shooting would involve fire forming your brass, but for 300-yard and under hunting, this would not be necessary. That Winchester brass will take some pressure.
I found that full-length sizing on every firing in the 7 Mag ALWAYS produced the best accuracy.
Those Light Weight Tikka's in 7 Mag has some recoil, and I would have a Gentry muzzle break put on the barrel before I ever pulled the trigger, reducing recoil to 243 Win levels.
The best accuracy will not be far off from what is the Max load for the rifle. For deer, some in my family shoot a lot of the Sierra 160g BTSP which is one heck of a short range(350 yd and under) deer bullet from all angles. The Sierra 160g HP Game King is one heck of a tough bullet, 160g Partitions are for elk.
OP, I hope this helps.