My first flathead v8 was in a 38 one ton express about 35 years ago. I ended up putting a 59ab in it, but know an 8ba is fine too. I later bought a '37 1 1/2 ton with an 8ba, and a '32 1 1/2 ton, also with an 8ba (just don't try to replace the fan belt)
,then a 47 2 ton that I installed an 8ba in. No fitment issues whatsoever. Since then it's been all kinds of 122" ford tonners, but primarily of the jailbar era ,'42-'47. Last winter I built a 276" 8ba and installed it in a '47 half ton pickup. Truck pumps and a one wire on a slingshot bracket. You will love that fresh 8ba. Grab it before someone else does. And we need some pics of that tonner express.
Here's a link to a video showing the 8ba powered '47 2 ton with no front sheet metal so details might be made out. There's other one ton fords and my 8ba powered '37 on my channel, so scroll around on it. My trucks are undoubtedly of the 'homespun' variety, but if you look past the dust and dents you'll see a lot of what you are asking about.
https://www.youtube.com/watch?v=Bsm-...ZpcnN0IGRyaXZl