Possibility of Inclusive Cuts at NLO?

I am attempting to use MadGraph as an NLO fixed-order matrix element generator and I seem to be unable to ask for the cuts that I want. My goal is to calculate the mass of a jet in p p > j j events through NLO in the jet mass. NLO in the jet mass actually means that there are up to 4 partons in the final state. With a non-zero jet mass cut, this can (in principle) be generated from p p > j j j events at NLO in MadGraph.

First, I'll describe what I'm doing to generate the LO jet mass distribution. I generate p p > j j j events in MadGraph, and then in the run_card make the following cuts:

 3.0 = ptj ! minimum pt for the jets
 650.0 = ptjmax ! maximum pt for the jets
 2.4 = etaj ! max rap for the jets
 0.0 = drjj ! min distance between jets
 3.0 = mmjj ! min invariant mass of a jet pair
 530.0 = xptj ! minimum pt for at least one jet

All other cuts are set to their default values. These cuts ensure that there is at least one jet in the final state with pT > 530 GeV (and less than 650 GeV), and the other partons in the event can be very soft or nearly collinear to a final state jet. These cuts are IRC safe, so everything is finite, and the events that are generated produce beautiful jet mass distributions down to very low masses (down to about ~5 GeV) when the values of the cut parameters becomes important. So this works at leading order excellently.

Now, I would like to do the same thing at NLO, to get the NLO distribution of the jet mass. However, the run_card for NLO event generation is very, very different than for LO generation. It seems like the only jet cuts I can impose are a minimum pT cut on the reclustered event. This is unfortunately insufficient for generating the NLO jet mass distribution. To do this requires essentially the same cuts as I imposed at LO, importantly with an inclusive jet pT cut of requiring that there is at least 1 jet (as reclustered with a jet algorithm with radius R) with a pT greater than some cut value. To get the jet mass distribution at NLO, I cannot make the cut that there are three jets, each with a pT greater than some value.

Is it clear what I would like to do? Is it possible to make more detailed cuts for NLO event generation in MadGraph?

Thanks!
Andrew