I think you’re overthinking this thing!
You’re making something simple complicated.
You can get a basic turkey cooking rig at Lowes or Home Depot for anywhere between $40 and $80.
A Bayou Classic or Masterbilt brand.
That’s all you need and they hold up fine.
Google “deep fried turkey cooker” for other options.
 
Don’t understand your math in the last paragraph.
You need 400 hot dogs–doesn’t matter if their 4/1 or 8/1.
You’re not going by pounds, you’re going by total number of dogs needed.
If you use 4/1’s, you’ll need 100 pounds of dogs.
4/1’s X 100#’s = 400 dogs
If you use 8/1’s, you’ll need 50 pounds of dogs. 
8/1’s X 50#’s =400 dogs
You need twice as many dogs if you use 4/1’s!
The only difference is in what it’s going to cost you to buy 100 #’s verses 50#’s.
Double your cost, double your price!