Before started to change payment processor maybe could be a good idea to try to fix current problem without switching from Stripe?

Just to let you know that there are services that handle VAT MOSS for Stripe automatically, for example: Quaderno $49/mo (I didn't try it).

Also you can try Paddle or Gumroard.

Paddle and Gumroard, the are both handle VAT MOSS automatically and you can choose rather you will pay (include in the price) or a customer (added as extra to price).

Gumroad and Paddle serving all your clients and you have just 1 client - Gumroard or Paddle that are sending you money:

Client 1
             \
Client 2  --- Gumroad (Paddle) --- You
             /
Client N

Gumroad:
- Fee is 3.5% + $0.3
- Can be withdraw only to PayPal (if you are outside US)
- Withdraw once a Week.
- Min withdraw is $10

Paddle:
- Fee is 5% + $0.5
- Can be withdraw only to Bank, Payoneer, PayPal
- Withdraw once a Month.
- Min withdraw is $100
- Tip: Paddle will charge 10% extra if they first payment wasn’t completed but they converted users with their auto email follow-ups. It’s called “Checkout recovery” — user opened email, clicked on the link and made a payment. But seems like you can turn it off

• Both accept payments from PayPal (your users can pay with PayPal). Stripe is not support it.
• Both have recurrent payments
• Both have API
• Seems like Gumroad is more fore Digital products (like apps, membership) and Paddle is more for SaaS. But it's not limiting you to use it opposite.

I would suggest to do the math and calculate how much it will total cost you for all 3 solutions:
1. Stripe with auto VATT MOSS service
2. Paddle
3. Gumroad

You can play around with different amount of transactions and prices.

Here is calculator spreadsheet for you: Make a copy

So you can make a decision consciously based on data.

Keep us updated which solution you will choose. I think a lot of people here have the same problem.

Good luck!