(6 * 8) * (7 +3) * 2 - 1 = 959
Is there anything better?
A fair bet, since I’d just have used the same generator anyway. 
(I wonder what criteria would be good for hand-crafting a really nice one?)
Working off of your own proposal:
(6 * 7 + 1) * (8 + 3) * 2 = 946
7 * 8 * (6 * 3 - 1) = 952
The only other approach I can see is to try to get to 951/3 = 317 with 1, 2, 6, 7, 8.
I don’t think it’s possible.
Attempting to get to 317 I can do (6 x 7 - 2) x 8 - 1 = 319 or (8 x 7 - 2 - 1) x 6 = 318.