Best shopping cart for using merchant account

I have the opportunity to gain a new customer who has a Wordpress website with a WooCommerce shopping cart. They have a merchant account through Elavon. Where they are currently hosting the credit card processing they use has stopped working after Elavon did some upgrades to their protocols. I have tried my best to work it out, but, the hosting company blames it on Elavon. My potential customer gets better rates through merchant accounts rather than services like Stripe or PayPal because they are in an energy efficiency field. She has also asked me about merchant accounts through US Bank.

So, the question I have for the forum is what is the best shopping cart for merchant accounts? I can obviously easily go the PayPal route, but this customer gets substantial discounts through other payment processing services.

Further: when it comes to hosting, are there any recommendations for vendors that offer up-to-date protocols?

Thank you.