If my 7mm-08 isn't under 1/2 MOA at 100 yards with reloads (139gr Hornady SSTs) I'll be disappointed.
Do you have a 1/9.25"twist or the 1/11" twisted Savage!
Let us know how it shoots the 139gr SST, we have been getting mixed reviews concerning the 1/11"twist in the 7mm-08. Some say they are 'one holing' with 139 grainers but most others who have purchased the new Savages with the slower twist have been disappointed as for accuracy.
As for the OP's question, I have several 116/16 Accustock/ Accutrigger rifles in varying calibers. They all shoot great, and I mean I have some stuff I put together custom, Stiller, Panda and so on, all sporter stuff we are talking, no bench, varmint or competition rifles, and all but one of the Weather Warriors will hang right with the customs.
While the Savage isn't a 30yr old Model 700 or Model 70, they are excellent rifles and the costs are not bad.
One word....follow your owners manual to the letter when setting the barreled action.
Follow the torque sequence and use the correct torque specs or the Accustock becomes moot. Torque values for all 3 screws is 40 inch pounds, executed in a particular manner. Also, put a dab of grease between the angled side of the recoil lug clamping wedge and the aluminum insert in the stock. Do not put grease between the wedge and the recoil lug of the rifle.
True the factory recoil pad is....well, it is mushy to say the least, but it soaks up nearly all the recoil.
You should get better groups than your getting now with an ammo change or reloads, I have not seen too many Savages that wont shoot sub MOA right out of the box.
Good luck with it, and enjoy!