...are their claims to "know beyond a shadow of a doubt that the Church is true" justified? Furthermore, is the Church's encouragement of such testimony bearing irresponsible? Why, or why not?
My opinion is that it is not given in this life (if you're theist) to have a perfect knowledge of anything, so that no-one can know with a 100% certainty on any religious matters. This is where faith, hope and charity come in.
I do believe that the church's encouragement (if they are doing that) is irresponsible, because it gives people the illusion that they 'know' something when really they don't.
To be really honest it would be better to say 'I hope that the church is true' or 'I have strong faith that the church is true', or even I love the church and the people in it.
Further on from that I think it is probably not very good to talk about a 'church' being 'true'.
Which part? Joseph Smith as Prophet? Which doctrine? (since they are subject to change)
The priesthood, the organisation? I think people should be encouraged to be more specific, and to leave out statements like 'the church is true' altogether.
Just out of interest, I always loathed fast and testimony meetings. I didn't like them at all and found them very hard to sit through. It almost always used to be the same people getting up month after month, mixed in with children being guided and primed by parents. Those giving testimony would usually end up spending most of the time talking about all the burdens fo that month... and exclaim through bitter tears that they were happy. I was never convinced.
I don't doubt the sincerity of those involved, I just don't think they are very precise, uplifting or intellectually and spiritually honest occassions.