Sounds like you have an early 110 made from 1959-1966.
The short answer is yes, it would be easier to find a different action unless you got that one for super cheap.
If you want to keep it, you'll need a bunch of parts. Off the top of my head, I'll try to type my way through it.
For the trigger you'll need: Trigger bracket, safety bar, safety bearing pin, sear pin, sear, sear spring, trigger, trigger pin/clip.
Bolt head. I'm not sure why they won't swap. It looks like they should.
Once you've swapped bolt heads you'll have to throw the barrel away as they aren't compatible with the modern style boltheads.
Here's some threads on Savage Shooters that explain what you have.
Controlled round feed