I don't know if this helps, but I've been running a subscription business on a squarespace for 4 years. The solution we came up with was an external app to manage the subscription side of things. It's slightly annoying in that I now have transactions happening on two platforms (squarespace and paywhirl), but it works fine, and every time I look at moving to Shopify I end up staying with my current solution because it's a lot cheaper for what I need. OP - I reckon paywhirl can do everything you're after. It's pretty customisable.
I keep looking at squarespace's subscription offering, but it really does seem pretty limited - has anyone actually seen any success stories?