You've been asking a lot of questions, and I assume to decide about a future purchase. For the requirements you say you want you have the best odds of finding it with a bolt action. With pumps, levers, and semi-autos a 1 MOA rifle is rare. You may stumble on one that will do it with one specific load. But you could spend a lifetime searching too. I won't guarantee 1 MOA from every bolt action, but the odds of getting there are much better.
It also seems that you're wanting something that can be fired rapidly. Quick repeat shots in a hunting rifle are WAAAY down on the list of priorities. If you don't get a hit the 1st shot, chances are not good of doing it when an animal is running away with the other shots. And with some dry fire practice, you'll be surprised at how fast a bolt gun can get off repeat shots. The difference isn't that great.
And you seem to be wanting wood instead of a plastic stock. Wood is fine, but there is nothing special about the wood being put on the vast majority of guns made today. Most of it is cheap and no nicer than what I burn in my wood stove all winter. If you want a rifle with decent wood expect to pay well into 4 figures. For me, if given the choice between cheap wood and plastic, I'll take plastic.
If you want to make this easy, buy a Tikka T3 bolt action. No fuss, no drama, no issues. Probably the most accurate, AND lightest rifle you can touch under $1500. And you might be able to get 2 of them for $1500.
They do make a version with cheap wood, but they are less common.
Choose | Tikka
Synthetic is available in blue for under $700
Choose | Tikka
And SS for around $800
Choose | Tikka