I have spoken to TaxJar about a week ago and they told me they are about to release an integration for Squarespace that would solve this problem. They said they are weeks away from it. For know, my problem is fixed because Illinois where I am based is an origin-based sales tax state, meaning I charge my local tax rate to everyone in the state of Illinois. Once we start getting more sales out of state and start having economic nexus in other states, then we will either have to get that TaxJar integration or move to a different platform (likely the latter, as I have learned Squarespace disappoints in many other aspects of e-commerce).
So my current fix to avoid having to add thousands of zips was adding Illinois as the state I collect taxes in and setting the state sales tax rate amount as my combined (state + local) sales tax rate.
Hope this helps.