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I'd speculate that, assuming they are synonymous variants, 返る would be preferred over 反る because its transitive counterpart 返す is so very common?

Very interesting. I remember a few months ago you brought that particular verb up in another discussion. I think that 開く with its two possible meanings was brought up alongside it. I have to say, however, as late to the party as I am (new baby has kept me busy and Japanese study has been little and long between, if such a saying exists), that when I saw 「かえる」, the first thing that popped into my head was 変える, which I noticed wasn't even mentioned in the initial post.

The reason for that is that in the 4th grade class I partake in daily, one of the first kanji they learned for this year was 変(へん), which included the 「かえる」 音読み.

I also wanted to say, along with my infinitesimal Japanese knowledge, that another kanji with two readings which stands out for me is 「角」. In maths (算数), the 「かく」reading is used (meaning "angle"), whereas is other situations, I'm sure that its 「かど」 reading would be more common (meaning "corner").

角 also has a third reading: つの (or 'horn,' as in on an animal's head)  

Ah yeah, I've come across that before, but at the time it never crossed my mind! Horn, antler, etc. Of course, it's a little easier to know whether someone is talking about a horn than it is whether they are talking about a corner or an angle. Of course, in maths it is often put together with 度, as in 角度. Pretty sure that's not the "degrees of a horn". :p

it can also be すみ as in 'corner' too, forgot!