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With the current system, you get the 2 factor authenticator and put the code in it will never work the first time, and it won't work anytime you take more than 15 seconds to click from the email window copy and paste the new code into the authenticator and then accept it. The whole things aggravating and annoying to deal with so I suggest making the code last longer. If you get an email give the man who's using that code 3-5 minutes before making it invalid or outdated and sending a new one.
30 is the default (https://tools.ietf.org/html/rfc6238#page-3) and using longer times only makes the system weaker and it's already not the perfect system, but it's simple and provides quite a good way of authentication.
Changing it to something greater than 30 would break every code for people using authenticator (some don't support different intervals at all, some would just have to log in and get new secret)
Allowing users to set specific periods is just an unnecessary pain in the *** for the developers and you still have a chance to request the code near the end of the interval so you get the old one.
Just use your phone or a desktop application to generate codes. Much easier and faster.