For example:
I am familiar with the word 日常（にちじょう）
I just came across the word 常日頃, and assumed it would be read じょうにちごろ, but no! It’s つねひごろ.
So that made me wonder, have you come across other examples of the reading changing a lot when the kanji are reversed? Feel free to share. 
Like this?
切腹
腹切り
Yes, that kind of a thing.
Slightly less gruesome examples also welcome. 
This one is slightly less or more gruesome, depending on your mood.
It’s less gruesome because it’s from WK level 15
It’s more gruesome because… what the heck, because Halloween!
人殺し and 殺人者
凹凸 おうとつ
凸凹 でこぼこ
BTW, I remember this by when you turn each kanji 90 degrees to the right with 凸凹 you get what looks like a D and a B for でこぼこ.
If it’s B and D, then it’s not でこぼこ.
before anyone else mentions it. it’s in wk so it’s a low hanging fruit.
登山 とざん
山登り やまのぼり
Then there’s also
干満 かんまん
満ち干 みちひ
… and I’m out of ideas.
規定 きてい rule, regulation, provision, stipulation
定規 じょうぎ (measuring) ruler
母乳 ぼにゅう mother’s milk
乳母 うば wet nurse, nursing mother
屋上 おくじょう rooftop
上屋 うわや temporary roof, shelter
物品 ぶっぴん goods, article
品物 しなもの goods, article
立腹 りっぷく
腹立つ はらだつ
日本「にほん」
本日「ほんじつ」
Surprised no one mentioned this pair yet.
Just encountered another one:
下地（したじ）
地下（ちか）