Hi Brennan,
I haven't seen Patreon used with Squarespace before but it seems like their pricing has higher % fees (starting at 8%) than the ones you already mentioned — are there specific aspects of Patreon they're looking to implement?
I guess you already looked into this, but Squarespace password-protected pages is an option since Squarespace can protect the pages from their side (more secure than the other options you'd be looking at)
Memberstack is a membership platform that does offer 1% fees or lesser, depending on the scale at which your client is planning to use it and the pricing plan that might best fit them.
Hope that helps!