You can look back at previous discussions about this topic in the earlier posts on here, there are plenty of discussions about this.
But Conn, Edwards, Getzen(cheaper than Edwards, but basically the same).
Why not Yahama?
You don't need Edwards. Go to Getzen's FAQ to find out why, Edwards horns are all modular, but thats the only difference from the Getzen horns, They are made in the same factory. Getzen's Custom Series horns are basically the best configurations for the Edwards horns. If you want the big bore the 3047 and the 42BO are two good options.
I just went through this with the help of my band director. We were after the 3047AF. We had a heck of a time finding one. At a point we went after the Bach, but were unable to find one of those. Getzen is not currently producing any new 3047's. We tried to find the Bach and there were problems with the factory and we were not about to wait for a retailer to get one. We ended up finding a 3047AF at a little family owned place somewhere out west. My best advice is good luck. Settling on a horn is the easy part. Big bore pro trombones are hard to come by for some reason, especially if you want a step up from the rotary valve, open wrap, etc.
If you can get the 3047 it's got about everything except factory problems. It's a very impressive horn, who can argue with 3 leadpipes and a Griego mouthpiece?
If you are fine with a rotary valve take a look at the Getzen 1047's, closest thing THEY make to the Custom series.
I've played a bach 42BO for many years. I recently inherited my sons Conn Lindberg 88-H. (I help buy him an Edwards). The Conn is a much better player horn than my 42BO(LTGC), I love it. My son loves his Edwards but still misses the Conn. I would recommend looking at the Lindberg, the trigger is even freer than the Thayer valve. Getzen makes a few really good horns, but if you can't get the Edwards, get the Conn.