If you are willing to mod the tunnel, then you might as well install an A518/A500; with their .69overdrive. If you can, get the one with the tighter ratios and a lock-up for sure. With 3.91s I would try whatever convertor it comes with.
here is what your automatic roadgears look like to the engine. This will be the regular TF with a lock up, and 3.91s
19.15>11.50-6.80-4.69-3.91 in L-up; cruizes at 65=3165
As you can see, 19.15 is ridiculously low, and 3.91s are a lousy cruiser gear.
These opinions all change with .69 overdrive, that shrinks your 3.91s down to 2.70. Cruizing in od, with 3.91s, should be around 65= 2180 in lock-up, a near perfect number cuz you can actually almost optimize the cruise timing for that.
I doubt your 340 even in it's present form would need more TC than what the overdrive comes with, right from the factory, which IIRC is about a 2400.
Just ask @TrailBeast how much he likes his.
Well yeah but, you won't be throwing that up there by yourself, lol.