As to the larger case here are a couple things to consider.
Out to 600m or so, against paper, it's not clear that you will have any advantage by going to a heavier bullet.
For across the course competition, David Tubb has come up with a new design, the 6XC, basically a 6-250. But, the brass isn't as consistent, and you burn quite a bit more powder. Cases this size and larger also appear to need a large primer, so you loose that advantage of the 6BR case.
RUAG has come out with a larger BR style case--the 6x47 Swiss Match. Thus far however, at least in 300m competition, it has not proven superior to the 6BR.
The closest thing to what you may be describing is something like the 6x44 wildcat, which was used by Joel Kendrick to set a number of 600-yard world records. There is a full write-up of the 6x44 on this site. The negatives are that case-forming is extremely time-consuming.
As for pushing a 140-grainer, many, many different cases have been tried. The problem is that these bullets have a long bearing surface so you need a good deal more powder to drive them. Though it is not ideal, the 6.5-284 is probably the accuracy king for long distance in the 6.5 caliber ... at least so far.
Coming full circle, once you move into heavier bullets, with bigger cases, and more powder, you start to sacrifice many of the advantages of the 6BR, namely low recoil, efficiency, ease of load development.
I should know. I campaigned a Rem 260,6.5-08) for 3 years. It would drive a 123gr Scenar about 2950 fps or a 139gr Scenar about 2840. Out to 600 the 6BR has proven more accurate, much more consistent, easier to tune, and it gives up very little ballistically. There are fewer brass issues with the 6BR, you get much less recoil, barrel life is longer, and it's less costly to load because you use 15 grains less powder.
Is the 6BR perfect? No. We think something like a 6mm Dasher with a long neck would be better for shoting long-range with heavy bullets. But it performs awfully well as it is, and in the 30BR format, nothing can touch it in BR score shooting.