I'm not sure how strict you should go, we have gone to the absolute maximum - and have to deal with customer service issues / abandoned checkouts daily. But even requiring the ZIP code to be correct made a big difference.

We're also using shopify which has helped quite a bit with their built in fraud analysis (Not 100% but I think it's either signifyd or kount providing the data).

Alternatively, you could use Paypal Pro to negate the account requirement?