You aren't going to to shoot the difference between a 7.5" and 8". Slightly more stability is always better then slightly not enough but in your case either will more than enough to get the job done unless you decide to try one of the heavier bullets which really don't suite the straight 6BR.
.236"-.237" flip a coin. I have both and both win matches. I get the same speeds from both. Zero difference in accuracy.
# of grooves, again records have been set with all of them. Pick one of the top tier barrel makers and go with whatever they specialize. They have dome their R&D to make their preferred number of groves work. Ford, Chevy, Dodge. You just have to pick one.
Contour, no effect on accuracy as far as the barrel is concerned but weight is moderately important for how the rifle balances which has a bit to do on how the gun handles on the bags.
Yes! It's all ver confusing until you have some miles on all of it. Really the biggest effect of all of it on accuracy would be not having enough twist, which at 8" or slightly faster you enough. You'll get way more out of LOTS of shooting and learning to keep it in tune than in thinking there is a Holy Grail of the perfect combination of barrel specs.
Certainly don't think there's a "holy grail" of perfect specs; never have. Just wondering what people's actual choices are with 6BR in practice, if seeking moderate accuracy at distance.
Twist / Stability -- Always thought slightly more was better than not quite enough. Uncertain if in the case of 6BR there's too much of a good thing, but all the barrel makers seem to specify in 6BR down to 1:8" or at most 1:7". I'm assuming they wouldn't offer it if it couldn't work. As others have suggested, with the barrel maker's recommendations and output from the Berger stability calculator, the weight ought to point to the proper twist. Obviously dependent on preferred bullet weight. I'm all for the 103-108gr "standard" bullet choices, out there, for LR BR, and suitable twist.
Bore diameter -- Seems there's a typical experience, that there's little to no practical difference with .236" vs .237" for the bore.
Grooves -- The few that have posted specifics seem to feel there's no difference between them. Good to know. Some have posted elsewhere that a particular one was worth worrying over. I've only done 4-groove on a prior re-barrel, so I wasn't aware of whether the various choices, these days, were worth evaluating.
Contour -- I've always thought, generally, that more steel (diam.) equates to greater stiffness. Assuming it's of a length that matches the caliber's harmonics. Though, as some suggest, it's probably far less important than balance, behavior on the bags, etc.
I appreciate the lists of equipment people have posted, from time to time. Helps for selection, at least, of make/model of choices, if not particulars beyond that.