New account registrations are currently either closed or very limited
If you do that, the psychology goes like this: "I wonder what this is?" (click) "Ooh, a new social community! I like those!" (reads further) "What do you mean, new accounts are closed or very limited? What if I want to join? Why are you gatekeeping me? Damn you!"... except with words stronger than 'damn'.
Once you're ready to let anyone sign up, email hn@ycombinator.com and we'll help you out.
But do you really need my phone number?
After xyz signups through it, make the rest of the day's accounts require manual approval for the first few posts.
You can also mitigate the disposable mail problem pretty easily by requiring whitelisting for any domain that's got more than a few accounts tied to it.
That comes out way cheaper for you, and might improve the quality of conversation (because there are valid reasons for anonymity and pseudonymity).
EDIT:
Also, bug report: the category row at the top doesn't overflow very well; on smaller window-sizes, there are many categories out of view. Maybe make the hamburger menu come up on more than just mobile screen factors?