Launch in closed Beta. Be upfront with the customers that you accept in your Beta program. They can be extremely forgiving with bugs as long as you inform them before hand and especially if there is no alternative to your service.
Choose the best 10 customers for a Beta 1 - and go through a rapid phase of issue fixing. Then increase the number of customers for Beta 2 by another 10. Continue in this fashion till all your issues have been fixed.
Choose the best 10 customers for a Beta 1 - and go through a rapid phase of issue fixing. Then increase the number of customers for Beta 2 by another 10. Continue in this fashion till all your issues have been fixed.