I can't imagine. It just sounds so unwieldy. There's just so much information in that non-canon universe, and so much of it conflicts with itself and the canon, that parsing through it all would be a nightmare.
So the problem is so hard we shouldn't try to solve it? I don't things as being that dire. I think a process like the following could work:
1) Submission - Productions would need to submit their own work to the non-profit organization in order to be considered. This would include supporting materials; if they want their ship to be considered part of canon, they need to include some kind of model or blueprint of the ship so that others could include it in their productions. Some productions could be submitted with the understanding that they will be distributed under a non-canon classification (parodies, for example).
2) Review - The submissions undergo a review period where the community can comment on the pros and cons of inclusion in canon and what problems the inclusion might cause. (I think a good review period length would be 90 days.) At the end of the review period, all comments will be compiled into a single document containing all relevant criticisms and benefits of the submission.
3) Qualification - A panel of experts would determine if a reviewed submission is eligible to become part of canon based on an established set of criteria (quality, backward and forward compatibility, et cetera). In addition, they would give the qualified submission a series of scores to indicate how well it met certain categories of criteria. An initial panel would be selected by CBS/Paramount for the first year, but would be elected afterwards. Only people who have made submissions ("submitters") would be allowed to vote for panel members. The experts could also propose amendments to the criteria, and the submitters would vote on those amendments.
4) Public Vote - A qualified submission would be voted on by the public. Voting would be open for a definite period (perhaps 30 days). The vote must reach a 60 percent threshold for the submission to be accepted.
Note that, in theory, there does not have to be a single canon. For instance, both Terminator 3 and the Sarah Connor Chronicles might be considered as being in their own separate canons.