How to handle taxes for Payment APIs/Stripe as a SaaS company?

We're currently a startup SAAS company with some revenue coming in. We have to pay out taxes and currently using Stripe to save the financial data using Tax Rates API so we can pay out taxes on our own. Our customers are in the US and also international like in Europe.

Currently we're using Stripe for payments and also using their Tax Rate API to construct the tax data that need to be paid out and then paying it out manually ourselves to each respective government. However it is a very painful process as we need to create a tax rate manually for each US state and province of any country we sell in it seems.

Is there a better solution for handling automated tax calculation and remittance for SAAS companies using payment APIs? Or any best practices that we should pay attention to? We're a new company and wondering how other mature companies handle this?

We also talked to Stripe Customer Support but I think we are beyond what they can help with there.

See: https://stripe.com/docs/api/tax_rates/create