If you are going Tranny shopping, I highly recommend a 3.09-1.91-1.39-1.00
This will get your 340 off the line pretty good with 3.23s. The first gear has 16% more torque multiplication, about equal to 2 rear gear sizes. If you get stuck with a 2.66 low, you would need 3.73s to equal the 3.09 x 3.23.
And 3.73s are none too hiway friendly.
The 3.09 low box is not a direct fit, tho, as I think they only come with a Ball & Trunnion output, requiring a replacement mainshaft and tailhousing
If you have an A833 with an overdrive, I call it a 3+1; but everybody else calls it an 833-od. Your 340 will not like this box, unless you put a 2bbl cam into it.The ratios are very far apart, and 340 cams are not revered for their torquiness.lol IMO it is the wrong box for a hi-rpm engine
I've been there,done that; and I ain't going back.