Re: battery box for house battery
That looks just like the battery box that my aux battery is in, in my 2009 gas engine E250. I have spent a lot of time measuring and researching this same question.
This battery box will fit a Group 65 (75 A-hr) batttery perfectly. For my van, there is room to add another box on the passenger side behind the existing one, but the frame will need to be drilled to mount it. A Group 27 (95 A-hr) fits into the box (I tried it at a battery store) but it is taller than the Group 65 so the lid won't fit and the box would need to be mounted about 1" lower for the Group 27 to clear the bottom of the step. However this would put the lower mounting holes near the bottom of the frame and that doesn't seem like a good idea. It would also put the bottom of the battery over an inch below the body. Another option would be to modify the box to be deeper, which would require cutting, welding, and sheet metal forming.
The nice thing about the factory boxes is they have slotted mounting holes so it's easier to install and remove with battery in it. They also have cables that prevent the whole thing from falling on the floor.
OBTW this same ebay seller has entire pallets of those boxes available, they may be open to offers...
2009 E250 RB 5.4L "SilVan"