i tend to take a different approach to cutting through with a jazz than most. i find the bridge pickup to be anemic and gross, so i turn it off. no more phase, no more thin nonsense. dial in a crap-ton of high mid on the neck pickup and remove lows or low mids as necessary to reduce boom.
touch of overdrive and played aggressively, im in heaven and bulldozing my way through the mix.
That's the tone I use when I play my Grind with a pick. It works especially well with the Lace Alumitone Bassbar I dun stukd in 'er.