You may be right, but we believe this will help us to make product of a higher quality and give attention to every single player.
I am sure it will. Its always better to not being too hasty when launching a new site. If the first impression of a new player is bad (site is too slow, doesn't work properly, ...) he/she will likely never come back and give you a second chance.
We understand that once open for a public we will need to work extra to convince all you to join and try the game
Do you consider hosting a signature campaign here at bitcointalk? In my opinion its a very good way to attract new players and get awareness. There are already a lot of gambling-oriented signature campaigns out there, seems to be kinda "state-of-the-art"

We plan to run signature campaign once the game is open to public. Running the sig campaign while game is invite-only is not very fair for potential new players.
Regarding your invite-only rule. You wrote quality over quantity, but how can you ensure that the people who registered on your site before the deadline date, or those who were given an invite have the needed quality to test the site properly? Do you conduct any research on the people who apply and send invites based on your findings?
Because if you don't, you can't ensure that quality over quantity standards are met.
No, of course we don't "evaluate" players who join, that would be quite arrogant from our side:) When we say quality over quantity, we mean that, e.g. we see new player registered, made a deposit, played and then left and did not come back for over X days - so we assume he did not like something and since amount of players either from DuckDice or joined by invite we always have a communication channel with that player, so we can go and ask him directly about his experience and hope that player will share it with us. Or other scenario, when we check hit maps and notice "unexpected" behavior we can conduct a survey. We have BI software of course, but talking to players was always important part of our development - so not qualitative players (we love them all), but more quality in how we look into our players game patterns to understanding their needs.
And since our players are either old DuckDice community members or people who explicitly asked to join they more likely to share their feedback and we know our community so we also we can understand the behaviour of players (and hopefully we will understand it correct

)
This may sound like a long blah-blah but hope you got the point.