Why wouldn't a multi-vendor non-profit organization remain independent? Independence is the only reason why most of them exist. No one trusts individual vendors to be neutral in matters like these, because there are obvious conflicts of interest.
However, as of today, there probably isn't a single independent organization that is set up to run an operation like this. So the vendors that care are likely to have to either establish a new non-profit key signing authority, persuade an existing non-profit like the Apache Foundation to take on the job (with the appropriate contributions of time and resources), or establish a private for-profit key signing model where multiple independent, for-profit KSAs (think Verisign) have the ability to validate and sign binaries on a fee for service basis.
As it stands, from a multi-vendor point of view, it is unbelievable how poorly this was thought out. It is so bad that the whole scheme could probably be shut down on anti-trust grounds alone. It is a de facto conspiracy in restraint of trade.