your price are quite high some members register and push domains for 3.5 or less , i'm able to register a domain with 0.99$ only for personal purpose it tires me a little bit register and register and register to get your domain :p
i will buy some domains from you if you reduce the price a little bit
good luck for your services
I also support the opinion that says the price offered by the OP for a non premium .com domain name is on the high side, i would patronize him if he reduces the price simply for the purpose of anonymous registration of a domain name.
In beta phase I have kept that price. and in the coming future I will try to reduce the price after going out of beta phase.
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I do not think anonymous domain registration is possible with godaddy. I guess OP offers flat rate which is good as it may benefit you sometimes also I hope you are already aware of namecheap's bitcoin acceptance.
I will buy the domain with fiat payment systems and will resell them to the buyers with bitcoin, so the system will be the same as godaddy has.