Well, XUSNORDIE has proved me wrong. I didn't remember that Ruger had produced a Mannlicher stocked .22 bolt gun.
But I understand your search for accuracy. AND,, the desire to have a gun that matches your preferred mate.
We do try to help folks here when we can. And heck,,, even offer advice on products outside the perimeters of the searching!!
I have a 77/22 and a buddy of mine had one. Both guns are accurate. Mine has a scope only sight system. His had open sights as well. I have used his 77/22 to win turkey shoot matches several times.
The American .22,, I can't directly attest to it's accuracy,, but from all I've heard they are quite accurate.
Heavy barrels vs regular barrels. One of the factors that makes a heavy barrel preferred is it absorbs heat & doesn't shift it's accuracy better than a regular barrel when a lot of ammo is being fired & heating up things. And,, a heavy barrel is often preferred to allow steadier shooting.
But if I were to wanting to use a .22 to practice with to allow me to shoot a larger calibered cousin,, I'd look at a regular barrel type,, to match the other gun.
Lastly,, each & every gun is a machine unto itself. You have to match the ammo to the gun to get the best accuracy. Plus,, quality guns do cost more in general. And since you mentioned "super accurate" as a criteria,, a lot of thought should go into your choice.
One of the absolutely top level accurate .22 bolt guns I've found,, AND at a very reasonable price (comparatively) might surprise you. If you can find one,,, a French made MAS 45 .22 Mauser bolt gun. It has a 5 shot magazine & was designed as a training rifle to reduce the ammo expenses for their military. Many were imported 30-40 years ago,, in crates. They are heavy & plain looking. Parkerized barrels & actions. A good sturdy Mauser action, and gosh awful accurate. Peep sights only,, unless you modify one.
Harder to find nowadays,, but I've had the privilege of owning one,, and shooting several of them. ALL were match grade accurate.
A buddy of mine & I were just discussing them the other day. He laments the loss of the (2) he used to own. And we both had extensive experience with them. I guess between us, we've sampled over 20 of them. All were pin-head accurate.