"Even if" and "even though" have slightly different definitions in the Longman Dictionary of Contemporary English*:
"even if is used to emphasize that something will still be true if another thing happens: She's going to have problems finding a job even if she gets her A levels.
even though is used to emphasize that something is true although something else has happened or is true: Even though he's 24 now, he's still like a little child. / I can still remember, even though it was so long ago.
In your first sentence, "even though" would impart a different meaning. It would mean that you do indeed know that the legislator in question does not agree with your position.
In your second sentence, "even if" would mean that you might meet that person, while "even though" means that you probably won't.
In other words, "even" intensifies the "if" or the "though," whichever you mean to use.
*Longman Dictionary of Contemporary English. New Edition. Longman. 2003