LMS Integration with SquareSpace website

Site URL: https://www.letterbetteracademy.com

Hi!
We use our SquareSpace site as the front door to our business. We are currently researching third-party software to run a virtual classroom and are having a tough time finding the right fit. We want to connect 20+ teachers to potentially hundreds of students, so we can't make Members Areas on SS work for us. We want the whole thing to integrate as seamlessly as possible with our Homepage: teachers and students log in through our site and find their schedules and classrooms without issues.
Does anyone know of any programs out there that have been successful? Examples are Ayotree, Themeum, Thinkifis etc.
Thanks for any help,

Steve

LBA

I'm curious to learn whether squarespace can integrate with LMSs, like canvas.