If it's out of the box accuracy and less tinkering time you are looking for, then I suggest you get a wood stocked Handi or a Laminated Ultra...though I believe the regular wood Stock is the only one availible in the 35Whelen unless you send off for an extra barrel.
The wood stocked Handis seem to be more accurate straight out of the box than the Synthetics, but not all the time. I have used both with sucess.
I guess sometimes we get so involved in trying new ways to keep our Handis shooting, and trying new things we sometimes forget that it might scare off anyone thinking they don't have a chance of getting a shooter right out of the box.
Welcome to Graybeards by the way. Enjoy the site.
-Aaron