“When I asked a different well known posek for his opinion, he told me (and asked not to be quoted), “You should be machmer”.”
Yes, YOU should be machmer since you asked for yourself, but the entire frum community need not be machmer since we did not ask this posek and since this posek wanted anonymity, it means that this Psak was for you only.
Being machmer beyond the ikor din is a personal decision. Everyone has their pet Mitzvos where they may want to be machmer, i.e., tzedakah; esrog; glatt; cholov Yisroel.
However, there are certain areas where one must be stringent, i.e., talking in shul; g’zeila; lying; loshon hora.