That is a common internet problem. It is not specific to your particular issue.
The only effective response you can mount is to:
1) Report all abusive posts to the moderator.
2) Reply to the post and refute the allegations.
3) Start your own website where you can moderate the posts.
By the way, most people just weed through the false posts and ignore them. So you are not being shouted down. Your views get heard and registered when you post them. Actively proselytizing your faith is not appropriate to the mission of this site. Such a response will probably get the moderators cracking down on you.
[even when it has been clearly and factually pointed out to them on multiple occasions that they are bearing false witness against our faith.]
How can someone bear false witness against a false faith? If I say the Aztec religious sacrifices were crazy, would that be false witness?
Indeed!
I'm sure that The LDS Organization® headquarters; based in Salt Lake City; probably has a little bit more money than JimRob has, and would be able to a really nice website; all it's own to proselyze with.
Of course, it would not be able to inject it's views into all things conservative that way.