The 888s are a good tire for the money, and do have an impressive amount of grip, while also being very durable. We were impressed with their performance at the 25 hours of Thunderhill, where we completed the shortened 17 hours using a total of six tires on our 1970 240Z with it's less than ideal strut suspension. It's worth noting that the remaining tread suggests we could have gone the entire 25 hours on one set of left side tires and two sets of right sides. The tire size was 235/50-15.
We ran lap times the equal to, or better than the previous bias ply slicks, a true racing tire, and in my opinion the grip character or feel was very consisent throughout a 2 hour stint.
We went to the enduro with no experience using the 888s, having never run the car on radials of any kind in it's entire 35 years as a race car, so the alignment settings were a sheer guess, and the target hot pressure was chosen from consultation with several PRO-3 drivers. Interestingly, the target hot pressure recommendation was substantially lower than the manufacturer recommendation, and our initial temp readings and eventual tire wear proved out the lower pressure recommendation to be valid.
One thing we did find interesting, and something that others have noted, is that the 888s have a dual tread compound, or something in their construction that results in an unusual tread wear pattern where a cupping occurs in roughly the middle of the contact patch. It wasn't an acute problem, but interesting nonetheless.
We also found that we were having a little bit more wear on the outside shoulder than ideal, even though we had maxed out the camber available at -3 degrees. This may be a problem for you, just as you are experiencing with the R6s.
The R6 is a good tire that is probably more finicky than the 888. It won't tolerate less than ideal chassis set ups as well as other tires like the 888, but will return a higher level of performance. In my experience, it can be a very durable tire given a chassis set up with good static and dynamic suspension behavior. I was personally very pleased with the performance of the R6 on the Viper, after I went to the trouble to cut off and relocate the suspension mounting points to improve the camber and toe curves. On a car that weighed almost 3400 lbs and made over 600 lbs of torque, I could run an entire season of 20+ sprint races plus test and tunes, using only two sets of tires total.
I'm sure I'm not saying anything you don't already know, but a tire switch doesn't really seem like the solution to your principle issue. It seems more likely to be a problem with limitations of your static alignment settings, and likely less than optimal dynamic camber behavior of your suspension coupled with excessive roll and pitch in the chassis, or other basic design challenges that will be difficult or take some effort and time to overcome. I honestly think you have an alignment or chassis balance challenge, not a tire problem, that switching tires won't solve. It may help the budget some, because the 888s cost less and will probably last a little longer, but they will be slower than the R6, no question, maybe as much as two seconds. And the construction features of each brand may be different enough, like the sidewall stiffness for instance, that you may find your problem of excessive outside shoulder wear only gets worse. Or, maybe it will be better.
The good news is since tires are a fairly high frequency consumable, testing something different doesn't really require any significant capital expenditure. I just wouldn't expect a silver bullet type result. My experience has been that it takes time to zero in on what a given tire needs, and switching back and forth confuses things.
My personal recommendation, which is worth a hill of beans, is to choose a tire that fits your needs best, and develop the chassis to suit that tire's needs. Maybe it's a good compromise tire for all conditions like the 888 that returns good performance in same, that's robust and a good value. Or maybe it's a more focused application tire like the R6 or BFG that returns higher performance in exchange for less service life.
My source for take offs has an easier time getting R888's in 245/40's vs R6 245/40 -- Sorry for the confusion.