Experience with 33s (smaller than you are going to run), 4R70W (less overdrive than the AOD), and a 351W that was a moderate build. Ran 4.88 gears.
With that, the unknown is the 347. There are unlimited ways it can be built and how it will behave. You don't see them built as a stock engine generally, Top end work, compression, typically sold by shops advertisng a HP number. If it is a mild 347, probably comparable to my moderate 351. Close enough I guess.
4.56 is out. Too tall. Something else to remember is the AOD also has a fairly tall 1st gear. So deep axle gears are needed.
4.88 would be a decent highway gear. I ran it with shorter tires and a lower overdrive. It was slightly over geared. I always said that my combo with 35s would be perfect. You have 35s, so that works. And if you were running a 4R70W I would stop right there. But that AOD gearset is different.
5.13s would be my pick. With the AOD overdrive it is nearly identical to the 4R70W with 4.88s that I said would be perfect. You still don't have the 1st gear I had with 4.88 and 4R70W, but the 5.13s will help get you closer.
I road tripped my combo from Phoenix to Vegas and back several times. It was actually a good highway cruiser. A blast to drive on the street as well.
Now if I can talk you out of the AOD and into a 4R70W, that would change the gearing down to 4.88s. The 4R70W is a much better transmission in so many way. I will say in every way. The AOD is garbage. They can be built to be strong, throw a ton of upgrade parts in it, you almost have one up to what a normal 4R70W is. The funky convertor bypass in OD changes into a conventional lock up torque convertor. Shift points is going to be a big one. Your 347 will not have a stock torque curve. So a stock set of shift points will be all wrong. The adjustments for an AOD for different shift points is very limited. For a 4R70W, no problem. Easy to work out all the shift points. Not just full throttle, but all the part throttle shift points as well. The only AOD argument that they are better is from someone who "doesn't want a computer". They don't realize the mechanical mess of the valve body is way more of a mess than the simple computer that runs the transmission. And even better, the 4R70W will still drive if you remove every wire from it. You only have 2nd gear going forward, but you still have reverse. Not like you are stuck to never move, like what can happen on an AOD if you get the TV linkage wrong.