Hmm... I honestly must not use my feet very much for climbing, because those shoes look fine to me. Now granted I mainly use 38mm brass, but I have also worn shoes with satin ribbons on 50mm chrome. I guess I use a different technique?
I started learning barefoot, but then I transferred to a new studio, where heels aren't compulsory, but everyone wears them, so I felt all short and dumpy as the only one barefoot. I found I needed to wear heels all the time to get used to them, and I slowly adapted. Even now I wear them at all time at pole unless I'm learning a new move where I might fall feet first. Here's some of the stuff I figured out:
With climbing I grip mainly with my shin and calf, which means depending on the weather I might need a bit of tite grip or shaving gel to help grip.
Things like star and cupid take a bit of practice to get the pole into the right spot. You have the inside of your calf and outside of your ankle on the pole. It feels really insecure at first and like your foot will just slip forward into genie, but it gets better. Maybe wearing heels builds your calves until they get big enough to get a good grip on the pole?
Balance is hard! I found a lot of it comes from the core. But your ankles also need to build strength of course
Standing up from the floor without the pole took me awhile. I found the trick is to stick your butt out. Actually,that helps in general, so again keeping your core engaged will help protect your lower back. But watch for lower back pain!
Everything is different and scary at first, so go easy on yourself, and take your time.
It might be a good idea to get some grippier shoes to start with anyway, because the ones you like won't be the easiest to use. I like to have nice shoes and practice shoes, because my poor shoes really take a beating. But I think they would be doable eventually, so there is hope!