I think you bought the wrong pair of 5.10s. I've got some Anasazi Whites
I specifically bought them for edging.
they have a thick(ish) sole area around the rim to provide better support when placing weight on the edges. I would suggest that the Moccasym's are a lot softer and are optimised for smearing on rough rock.
5.10s are known to be more comfortable, softer shoes, but I've also heard they tire your feet out faster
I'd dispute this TBH. 5.10 rubber is softer (stealth rubber). This is to aid friction not to make them more comfortable. What makes shoes more comfortable is buying the right shoe, regardless of make.
Every shoe will fit differently and everyone's feet are different sizes and shapes so it's hard to give advice in this area. Try on lot's and lots of different shoes and see which one's work for you. Look out for "hot spots" (where the foot feels hot in a
particualr area). This is a sign that the shoe is a bad fit in this area. I wear my 5.10s tight. They're 2 sizes smaller than my street shoes but different people opt for different options in this regard.
You want your toes (somewhat compressed) in general. This aids your ability to place weight though your toes. How compressed is a martter of preference, it's about balancing comfort with performance.
More compressed =
less compressed =
How do I make sure I'm building strength in my toes and mitigating
You can't really build strength in your toes. There is no major muscle in your toes to build. This is why your shoes support your toes. I would suggest trying to train your toes is a waste of time.
If you're experiencing pain, The culprit is probably your shoes. You may need to buy a new pair. This could be because they are too tight, compressing your toes too much or too loose, not supporting your injured toes enough.
It's impossible to tell this from here. I would suggest going to a good climbing shop or local climbing gym and talking to someone experienced who will be able to offer advice based on your current shoe and foot shape, etc.
This article may provide some helpful insights also
Climbing shoes: is pain insane?