I've noticed that I don't see 〜ましたり used very often, but it does seem to be an accepted form. I believe this form can be broken down like this: 動詞{どうし}の連用形{れんようけい}+「ます」の連用形{れんようけい}+「たり」
My understanding is that normally the sentence-final 動詞{どうし} is the one that is responsible for indicating the politeness of the sentence, while other verbs can be made polite depending on "how polite" you want the sentence to sound (as long as that 動詞{どうし} is not in a relative clause, and not in the objective clauses of certain verbs).
However, 〜たり makes a 動詞{どうし} nominal, so it is not clear to me when, if ever, you should use the polite form of the 動詞{どうし} when attaching 〜たり. (On a potentially related side note, I don't think I ever see the polite form of a 動詞{どうし} when using 中止形{ちゅうしけい} either.)
used very often
? Where do you hear it often? And probably like the masu-form before ので not being grammatically correct. Places where it is common to over-praise interlocutor (ex: 大丸), over keigo is usually used.