You are pretty much repeating my high school life. Ugh... not my favorite memories.
During my lunchbreaks I would wander between all of the groups my single friend within each of them hung out in, before wandering onto the next one another single friend in a large group hung out with and so on and so on. This was basically how my "friend circle" worked my entire school life.
None of them were really good friends with any of my other friends. And in their group I really only got along with them and no-one else they were friends with.
Anyway, late high school sucks for making new friends. Pretty much everyone is "locked in" to the groups of people they are friends with by that point... and very little shifts around.
There are the occasional options of new kids that come to school that year, perhaps foreign exchange students or something. But otherwise it is way too difficult to "elbow your way into" new groups in your school by that point.
Which basically only really leaves 1 other option, which has already occurred to you. That is to look outside of school for potential friends.
I don't know which state you are in, but in my state the local libraries have many groups doing many different things. Some of which might be of interest to you. Many of them run outside of school hours because they are designed for school kids... and depending on which library you go to, there is a good chance that they are people that don't go to your school. Many of these are free and not overly time consuming.
However, the most interesting ones I have found are "one on one conversational" interactions. This is basically an appointment between you and 1 other person (inside of the library) and is basically just talking for between 30 minutes to an hour about whatever you want (no expectations, nothing intense. Just casual conversation).
There are 2 types of these. One is with aged people... which I'm guessing you would not be overly interested in.
The other is with people from overseas studying in Aus. They speak English but need to practice conversational English with locals to improve. So casual talking is required. You learn about their culture, their country and they are super keen to talk with you because it helps them. They also have limited Australian friends yet, so if you get along you can organise conversations with them again in the library.. and if you both click over time. Potential new friend.
It's a safe way to meet interesting new people who are very different...