The second moment of area is quadratic with thickness (t^2), so 250/8" plate. But in reality 2-3x more than that, because at that scale steel gets a bit... goopy.
I saw a guy weld 1.5 or 2 inch plate once to repair the bucket on a giant bulldozer. That was… interesting. I was trying to figure out why he left such a big gap until he started welding. He had to fit the head in to lay down layer after layer of welding bead to join the pieces at full depth.
For a butt joint V it out on both sides and do many, many passes. Maybe have a few guys with rosebud torches working heat into it as you go. Big rods make it go faster (https://youtu.be/j61ezBX-EyA). For a lap joint it's the same idea, you're going for a great big fillet. But if you have a gigantic press at your disposal there are other options. For inspiration: https://youtu.be/k_LA_R4ifYk
The idea behind forge welding is you get both parts nearly molten (e.g. "welding heat") then your hammer blow (or the pressure from a huge press) puts enough energy into the weld area to briefly melt it.
Also, hot rivets might be a better option than welding if you can get away with it.
