You have a few options for this.
Years back, the NSSA ran/oversaw a winter league. You would keep track of the targets over the course of the event and submit at the end. I don't think they run this anymore though.
You still have a number of choices.
First off, you need to decide how you want to run your league. It can be registered targets or not. It could be registered for those who want to register, and not for those who don't.
There is no requirement to actually register the targets with the NSSA, although that could be a draw for some shooters.
It does not have to be all 4 gauges unless you want it to be that way.
I think that the easiest way to do this currently is to use the monthly targets option. You simply record Name/NSSA number/Class/Score and submit that at the end of the month.
There is a classification called 'Event 6' which pretty much lets you 'count' targets any way that you would like. The targets count towards a shooters lifetime totals, but not towards any individual event.
I know the NSSA is working on a new 'event' which may work as well, but I don't know if it is quite ready to be deployed yet.
I'll check with some people to see if they have any better ideas as I focus more on the summertime events rather than the off season options.
Feel free to contact me if you would like to discuss further.
Brad.