Kaiji is not likely to get licensed for a US release anytime soon, much less have an English dub along with it, but here's a few of the roles I have in mind if it did.
Kaiji - Dante Basco - sample How do you replicate Hagiwara's masterful, distinct performance? Answer: you don't. Instead, you go for something that sounds different, yet manages to convey the same character. Basco is splendid at conveying raw anger as well as vulnerability, oftentimes at once; the essential elements needed to play Kaiji's character effectively.
Ishida - Liam O’Brien - sample If you watch the clip, this one should (hopefully) be mostly self-explanatory. It's a bit of a typecasting decision on my part to assign O'Brien a gentle character with a hidden strong side (see: Vincent in Ergo Proxy, Kariya in Fate/Zero, Tenma in the Monster clip linked) but I think his voice would really fit Ishida like a glove.
Tonegawa - Keith David - sample Deep, smooth, and intimidating are the necessary traits to play Tonegawa, but there also needs to be something luring, even a tad seductive about it. You need to constantly be taken in with what he says in more ways than one, and David absolutely nails that to a T.
Hyoudou - Mako - sample It took me ages to figure out who would be the perfect voice for Hyoudou. I entertained the idea of Tim Curry, who stands alongside Keith David in perfecting the deliciously sinister-sounding voice, but as big a fan as I am of Curry, it still didn't feel quite right to me. It wasn't until I was Skyping with a couple of pals that it hit me that Mako would own that role. Sadly, this talented actor is no longer here with us, but, this being a dream cast, it's just a cool idea think about.
(Said pals I Skyped with also pointed out that with Basco and Mako in the roles they're assigned here would mean we'd be seeing Zuko and Iroh as mortal enemies here, too.)