I'd like to add some comments on this as well as a developer (not involved in GWT or Tapestry), specifically to address the bad feelings players may have about not being able to access a game. First I should correct some terminology that may be contributing to these feelings. The process is not referred to as "Secret Alpha". I can't speak to every project, but generally the developers aren't trying to make some exclusive club that you can only get into if you have the right connections. The whole reason that so much time and effort is going into developing and testing the game is so that everyone will be able to play it at some point. "Pre-Alpha" has a different meaning, and refers to the period of time when the game is under development and is not being tested by others. The term that BGA uses for this process is "Private Alpha".
There are multiple reasons that a game will be in private alpha:
The content of the game belongs to the publisher, and the publisher has the right to exercise control over the time and manner of its public release. As with Splendor, it's possible that GWT might pass over Beta and go straight to stable release, which makes for better press.
Alpha and Beta testing are different things, with different expectations of testers and a different level of attention paid to reports. Almost every game module on BGA is developed by a single person, who might only have a few hours per week available. It is a much better use of their time to fix bugs and improve the implementation, rather than wade through pages of duplicate and non-bug reports, or respond to an onslaught of messages from people who want access. It is best to keep the signal to noise ratio as high as possible.
For Alpha, testers should understand how BGA works and what causes may underlie the unexpected behavior so they can submit a useful report to the right channel. It's much more useful if Alpha testers play in ways to try to break the implementation and find bugs, rather than playing competitively. More testers does not necessarily equal better testing, and being enthusiastic about the game does not mean you will be helpful to the Alpha testing process.
During Beta, the process for very popular games relies on the wisdom of the crowd to prioritize issues via the voting system for bug reports. Inevitably, the general public will report duplicates of bugs that have already been reported, report non-bugs that stem from a misunderstanding of the rules, or ignore legitimate bugs, or post them in places they cannot be tracked.
As Tisaac said, there isn't a secret forum or channel you can find and post in that will change any of the above. The only thing accomplished by repeatedly asking, or finding different and more intrusive ways to ask, is taking time away from the developing and testing process. Please be patient, and let the developer(s) work on the game.