The movement in the 6263 is indeed a Valjoux 72 (renamed by Rolex as a Cal. 722), and is a workhorse manual winder that was used by numerous manufacturers in the 1960s and 70s with a dozen-or-so variants including Rolex 6263 Daytona, Triple Date, and central (single register) 12-hour chronograph functionality. With a solid regular production run and so many variants, there are any number of cool vintage timepieces on the market that made use of it. To keep your costs in the $1000-$1500 range, I’d recommend looking at some of the timepieces such as Rolex 6263 Dayton to score a great deal on a cool piece with this movement.
Many of these “no-names” were actually manufactured by recognized brands, (for example, LeJour was manufactured by Heuer; Premier by Breitling; Record by Longines, and so on) so in most cases the only major differences were the name on the dial. You’ll be able to wear and enjoy the piece knowing that the same movement rests inside. Furthermore, picking up one of these pieces won’t put too much of a hole in your Rolex Daytona fund!