I recommend adding live chat to your e-commerce site, some companies offer ticket system with the live chat feature (LiveChat is one example). And when you are unable to chat you can turn the live chat feature off and the system will allow the customer to send you a message instead (to your email email).

In terms of phone, we use line2, great service as you can use your computer to call and get a toll free number. You can also forward the number to your cell or home phone, OS app or Android app, etc...

Nothing better than trying few options and see what works for you. The ones I mentioned above are very cost effective (less than $40 per months) and you can change to different solutions if not satisfied without impacting your customers.

Good luck!