What I do not like at BTCpay payment page is that is redirecting the payment to your node location, where is installed BTCpay (if you have your webshop separately), so is not doing the payment in the same page.

Another option I think about for you is to use Lnbits with your tor node.
Lnbits is NOT redirecting the payment page and have a simple woocommerce plugin.
I wrote here a simple guide about how to use it.

If your webshop is already done, on clearnet and hosted on a separate server/domain, but you just want to add the option to pay with BTC/LN, you can do the following:

• install a Lnbits instance on your tor node
• configure Lnbits nginx to be accessible (only for your shop) through clearnet so the woo plugin can connect to your node directly.
• configure the woo plugin with your lnbits details (is very simple)
  Done, now you can use your tor node with a frontend webshop on clearnet without revealing your node IP.