Punch is, to me, upper bass and low mid girth (100hz-200hz). Unfortunately, depending on which Markbass head you are using (i.e., one with a fixed low mid center point at 380hz), it is hard to dial in some forceful low mids of your cabs or bass don't provide that.
A Jazz bass is also a bit widely voiced, so that combination is not inherently punchy. One thing that VERY much helps is to dig in a bit relatively close to the bridge, which naturally reduces deep bass and bumps up low mids and mids. Rolling of just a touch of the neck pickup can help also.
With the LM heads, stay away from the VTC, and don't boost the bass, dig in a bit over the bridge pickup, and you should have most of the punch you need. If you have an MB head with semi-parametric mids, dial in a bit of boost at around 200hz (9 o'clock or so) with the low mid control, and possibly roll back the bass control just a smidge.
Mid voiced roundwounds (like some nickel strings or the DR Lo Rider SS as examples) can also help.
IMO and IME!