Very powerful words.
“Does one who is orthoprax (I believe that’s the word used to describe the folks you are talking about)receive any sachar for the mitzvos that he is performing, albeit by rote and not by conviction? “
Yes. You get sachar for every mitzvah you do, even if you HATE doing it (unless, I suppose the actual mitzvah involves love, such as V’ahavta l’rayacha), and in fact, lifum tz’ara agra – the harder it might be to do the mitzvah, the more sachar you may earn for still doing it. Who cares (well I do, actually) if you give tzedaka by rote? At least you are giving it! So what if you fasted on Yom Kippur because you ALWAYS fast on YK? You still fasted. Is it better do feel the conviction rather than do things by rote? Absolutely. But is it still better to do it by rote than not at all? Absolutely. Having no kavanah but still following the Torah, will always be better than not following the Torah. And we DO believe that m’toch shelo lishma, ba lishma. And do not forget that even when you do not see the positive ramifgications upon yourself, doing those mitzvos impacts other people’s lives also.