I think the situation that Rick is describing is happening because in their MM operation, they work a lot of stations who are casual participants that aren't all that interested in QSYing to another band for a QSO like a more serious participant. They are just helping out by handing out a QSO.

Maybe a way around this is to have the NQ4I operation use W4AN as their callsign under the banner of being the sponsoring club of the GQP. Offer those who work W4AN 10 bonus points per band/mode contact. You could also offer a certificate to those who work W4AN on a certain number of bands to satisfy those who like to collect certificates. I have seen many other QSO parties that do something similar to this.