Dr No[Moderator Omega - Wristscan]
37672
I sensed the integrated bracelet . . .
. . . aspect of the RO and the Overseas designs were what you were after! Yes, there is one integrated design that fits within your budget . . .
. . . the Omega Constellation Double Eagle chronograph. Unfortunately, I only have this photo of one equipped with a rubber strap, but it is available with an integrated steel bracelet.
There's a limited edition titanium model from 2008, the Mission Hills chrono . . .
[photo courtesy Tony A]
. . . that's still listed on Omega's website, so it should still be available. I was considering this for myself at one time. It's probably the most comfortable watch I've ever tried on, and I'm taken with its stealthy appearance. Not everyone's cuppa tea, but one to consider.