In 1k comp high BC is not that important. Quality of the bullet and case is premier. There are a few who still use the 240, but most use either the 210 JLK or Berger or 216 Clinch River as 2x better quality almost same BC.
However, if you want to go to the 240, then either the standard Weatherby or one of the Weatherby improved would be best such as the 300 Ack Imp. The 300 AI is the one of the hot calibers to use. In 1k BR quality of cases matters, so skip the ultramags and stay with the weatherby case.
The 300 WSM is really good for 1k also, but at the 190-210 gr level and 1-11 twist. I have been shooting the wsm in comp for 3 yrs (light and heavy). This year going to 1-12 twist with the 187 Bib (flatbase) bullet. The 300 WSM with a 30" barrel can get a 210 to right at 3000 fps, but not a 240.
The 240 will require a 10 twist (do not use the 9) in the weatherby type cases. Suggest the Broughton 5c barrel and the 300 AI.
Suggest you talk to couple good 1k smiths, Bruce Baer, Leonard Baity, John Myer, Mark King on the east coast. Them and others can be found on recommended smith link at www.6mmbr.com.
Those 4 are very familiar with the type cases you are talking about. 300 AI dies are avialable from Redding also.
You can either build a light gun or heavy gun. Suggest either a custom action such as Python ($950 with tapered rings and trigger guard) or barrel block. The custom action is by far best way to go in the long run.
Mark King in PA. He is building a complete heavy gun with tapered base for around $2400-2500 and that is on custom alum stock and 700 action in barrel block. Stock is made to come in different colors and is really one of the best buys out there for building off a 700 action. He is about $800-1000 less than most for that type system as he makes the stocks. A typical HG system can easily run $3000-4000 so his is a bargain and a proven shooter. Rail system is built into the stock. He is another very good smith that is building some of the best guns for the PA crowd. He won one of the classes last year at the IBS Nationals.