It depends on what you want it to do. 35" tires are serious, but most I see are on vehicles that are spotless.
If this is for show, I'd do whatever is needed to have the new tires fit and re-gear the differentials to help preserve the older engine and transmission, and leave it. This will reduce much of the stress of moving those heavy tires, particularly on inclines, which will reduce the need for down-shifting. You might consider a new torque converter to induce more torque for acceleration from stop (a reputable transmission shop can work with you to determine the appropriate stall speed for your setup).
If the intent is for (serious) off-road use, what type - rock crawling, pre-running, back country driving, access to remote areas? Ideally, these would have different suspension setups (springs, shocks, anti-sway bars), a torque converter and maybe some form of locking differential.
Differentials come in several varieties - open, limited slip, selectable locking (electric, pneumatic, manual) and full-time locking. My preference is open with selectable locker because it provides the tracking of an open differential for on ice and snow with the full lock for off-road dirt and mud. A second would be open in front with limited slip in back with selectable lockers front and rear, or perhaps only in back.
