Your choices aren't limited.....you are limiting your choices.
Don't be afraid of clubs that require sponsors. Most clubs have public events. Go to a couple....introduce yourself......It gives you a chance to see what the club has to offer and a chance for a few members to meet you and you can usually get a sponsor that way to almost any gun club. You may have to put some work into getting a membership at a gun club.....if your not willing to put in a little work then just pay by the hour at rental ranges.
All that said....
Country pond fish and game Newton nh isn't terribly far from you and is not capped.....and has plenty of public events to attend to get to know some people.
A sponsor is like a college degree, it filters out a lot of people.
Some clubs make it easy, for example Old Colony, you show up to the monthly meeting and someone says they will sponsor you. Easy. (At least thst was the way when I joined around 2011).
Others, like Reading, actually ask the sponsor to write some information on the application, making it a little harder.
That being said, there are at least 5 NES members at every club in MA, make friends, get to know people and you will get a sponsor / recommendation.
It does take some work, but people here are great and will help you out.
Go to a meet and greet, show up to competitions, meet people ... they will eventually become good friends you are glad you met.