Seems reasonable.
At some stage we need to address the dislocation between what the kokugos say and what Japanese people actually use.

I note that for 続けざま, Meikyo has "多く「━に」の形で、副詞的に" (as opposed to a 形動 POS like Daijr and Daijs). So we could do this. But we need a consistent approach. The kokugos often don't agree with each other. Meikyo has ありてい as "名・形動" while in Daijr it's just a noun with a "多く「ありていに」の形で用いる" note.

@@ -15,0 +16 @@
+<s_inf>oft. adverbial as 〜に</s_inf>

That would be a departure from our usual way of doing things. See 続けざま, 苦し紛れ, ありてい, トントン拍子, けちょんけちょん, 我勝ち, あだおろそか. They're all usually adverbial with 〜に (and in some cases adjectival with 〜の) but rarely 〜な, and we tag them as adj-na.
Our description for adj-na is "adjectival nouns or quasi-adjectives (keiyodoshi)". I think our use of adj-na should conform with its actual meaning, not what people mistakenly interpret it to mean.

形容動詞 may not strictly mean "used attributively as 〜な" but that's obviously the implication of our tag "adj-na" and exactly how the absolute majority of our users will interpret it, and I wouldn't blame them for it either. I don't think it's helpful to tag this entry as adj-na when it's obviously the case it's NOT used attributively as -な but only -の. I feel fairly sure we have other entries tagged adj-no and not adj-na which can be used adverbially withに. Actually the very first search result in jmdictdb for "adj-no" is 100倍, which seems like a perfectly good example of this to me. 

So I do believe adj-no does also imply -に adverbial use and that -に usage being widespread is not a particularly good reason to tag the entry as adj-na if it's already adj-no.

> に is implied by adj-no just as much as it is by adj-na, no?
I don't think so. "adj-na" doesn't mean "used attributively as 〜な"; it means "形容動詞", which 思い通り is, and there are plenty of 形容動詞 that are almost always used adverbially.