Approach shoes for narrow heels

...here we go again. So, (story of my life:) I can't find shoes that fit both my foot length (size 112.5/13 US) and width (extremely narrow, especially in heels). I'm trying to find a decent pair of Approach shoes for...well, approaching (and light climbing), but everything I've tried is either too short (toes at the end/rubbing against the top) or too loose, causing heel slippage. I thought 5.10 would be the ticket, as Anasazis fit me perfectly, but alas...my heels were visibly slipping out of the shoe in a size 12 Guide Tennie. Also tried La Sportiva Boulder X, and it was worse. I do have a pair of Merrell Moabs that are super comfortable (very slight heel slip), but I'm hoping to find a more technical Approach shoe. Any ideas?

I have a fairly narrow heel, and I found that the Scarpa Crux worked well for me. I'm also looking at trying out the Adidas terrex or the Sportiva TX2 after winter.

Cool, will try those.

My Evolv Cruisers are very narrow. Super light, super compact. I really like them and have done alpine approaches up to 6mi (round trip) with them, very happy.

Cons not water proof at all, and so thin that kicking a rock accidentally hurts more than in comparable sneakers.

I have a very low volume foot. The Sportiva Boulder X fits my narrow foot well. They are quite stiff and are almost more along the lines of a low top boot. Some people aren't into that sorta thing but I love them. $86 on Back Country right now