I can't help with a phone number, they don't seem to provide one unfortunately. Now I have heard some people say they are quite happy using EZ, but, and this is only my personal opinion and I have to say that I have never dealt with them myself.
I would be asking myself if I really wanted to deal with a supplier (especially a drop ship supplier) who offers such slow customer service and very limited access to that customer service.
No phone contact means that you are reliant on email as your support hotline. If you think it's frustrating waiting for them to respond to your past 5 inquires now, imagine how frustrating it would be waiting to have your emails responded to if you were trying to sort out an issue for one or more customers.
It's a point that is often over looked by many when choosing to do business with a drop shipper. The focus is more on price, more so than on the customer service they provide. When you are using a drop ship business model, the customer service you provide to your customers is only as good as the customer service you are getting from your supplier.
If they aren't providing you with quality customer support, then it's your customers that will be effected and anyone who's been in business for any amount of time will usually know that providing your customers with bad customer support results in very unhappy customers who are then more than happy to make sure they do as much damage to your trading name as is possible ..... and that's never good for business.
You can't just say, I'm sorry, I'm waiting for my supplier to get back to me. Customers don't want excuses, they want answers and solutions to any issues they feel they have. The fact that you might be having trouble getting in contact with your supplier will be of no concern to them at all, nor should it be really.
So, end result is that it all washes down hill. You get bad customer support, you deliver bad customer support and your business is the one that will suffer for it.
As I said, not a personal reflection on EZ, but I am frankly sick to death of the pathetic level of customer support some companies provide their customers. Why customers seem prepared to accept that is beyond me, but I know well that it will never change while they can get away with it.
Just a thought :)