How can I send SMS messages from my Google Voice number without using the Voice app?
This isn't the cleanest solution, but it's an option:

If you set up your google voice number so SMS messages are forwarded to your phone, every time somebody texts you, you will receive that text from a 406 area code phone number.  If you send  a message back to that number, it will reach your that person, and appear to them as if it came from your google voice number.  So you can save the 406 number for each contact as a secondary phone number, and set it as the default number to use for SMS.

(if you think the Google Voice app is cumbersome, you should try doing it from an iPhone ;) )