Age of the rifle, and who produced it?
Sounds like tension issues w/ expanding metal. I would probably disassemble, and reassemble paying close attention to tension and retry. I am not a huge fan theoretically of no tension on the barrel/having no support, but admit I am not read up on it. These guns were not meant to be 'free floated'
Does the rest of the rifle 'line-up'?
Ordinarily I would say a 3-4" group at 100 is normal for a lever, or at least it used to be, but that is a big jump from one shot to another.
Also you will be giving up a decent amount of velocity for 35 Rem at 16," which you probably already know. Would probably be fine for 200gr core-lokts, but not every 35 cal bullet is designed to expand at low velocities.