The OP is looking for a rifle with a larger diameter wrist. It is his finding that those rifles he has handled would not shoot well for him because of this.
How about a do-over. Any stock can be lengthened. Some won't look particularly nice afterward, most people will recommend a recoil pad. Consider whether you will be hunting (and your climate) if you opt for that as a rubber pad can snag on bulky clothing when shouldered. When given the option on custom stocks, I opt for an extended length of pull. I've found however that even stocks sized for children can be shouldered comfortably, especially with the use of a swing. The more you concentrate on fundamentals and the shot itself, the less a concern there is about the firearm you're shooting.
On the wrist or "grip", I keep my thumb straight rather than wrapping it around. Some people opt for a new stock with a swell or add a pad or tape to build this area up and/or to add a bit of traction. I've read a number of threads, usually dealing with handguns, that speak to grip size and the comfort level of a given single-stack or double-stack. For those with interchangeable inserts I generally preferred the largest grip available but found the smallest insert on each universally improved my accuracy.
As to which rifles out there will have a large enough wrist to meet your criteria, the AR style .22s mentioned may be your best bet. Whether you'll be satisfied with them can only be determined by you. If you lean that way, Ruger does make a 10/22 in such a configuration that is considerably less expensive that most.