Where do you see that adapter on Advance Adapter's site? I cannot find it.
The main issues are going to be:
1) Shift pressure calibration. The A440F is a "medium duty" transmission designed for trucks, but it has been calibrated to shift very smoothly and softly behind the relatively weak 3FE or 1FZ. A V8 will likely toast the clutches very quickly without valvebody work. A diesel valvebody might get you the holding power you need.
2) Shift points. The 3FE isn't a particularly high revving engine - most small blocks rev higher. The transmission will likely short-shift your engine in most applications. This problem would likely be made worse if you swapped a diesel valvebody.
I wouldn't say either one of these problems are insurmountable, but it would definitely take a lot of valvebody fiddling to get right. It's also entirely possible the A440 would just never be able to reliably hold the power of a V8 as-shipped by Toyota. That's why most people just use the GM transmission instead.
An example of this: A friend of my mine swapped a Toyota 1UZ V8 into his Jeep. It turns out Jeep uses the same Aisin transmission as the Tundra and Lexus LS400, and you just have to swap the Tundra or LS400 bell housing on to the Jeep transmission. Well, it worked, except WOT shifts were terrible. You could tell the transmission really struggled to grab the next gear. We ended up having to put a shift kit in it, and it was fine after that.