Saddle fit (for the rider)

Looking to educate myself!
I’m relatively new to the dressage world (coming over from jumpers), currently on my second dressage saddle, a Custom (blanking on the model at the moment but it’s a monoflap). Bought it because it fit my horse very well and fit me ok. As I’m progressing in the discipline I’m noticing more things I struggle with, most specifically being able to keep my lower leg on my horse (who is a relatively narrow barreled Hanoverian). My trainer gets on me constantly, and every video of my rides I see how my calves are probably 6” from my horse’s sides. I have a very stable lower leg, but trying to keep the contact on her sides pulls my thigh off the saddle and brings my lower leg back. I have an easier time keeping the correct contact and position riding without stirrups, so I suspect the stirrup bars are too far forward for my body structure. My legs also slide forward - not into a chair position but definitely forward of my hip (again, not an issue without stirrups). Additionally, my saddle has a very definite center of balance, and it’s very comfortable sitting there, but my body goes forward that point while riding (even walking) to remain balanced.
I want to start looking for a new saddle that fits both me and my horse, what are some things that sound like they may be a problem so I can bring this up with some reps? Saddle size? Twist size? Specific things I should be asking or looking for?

Honestly I think you have to sit in a bunch to figure out what you like. After many years, I know I prefer a more open seat, if there are thigh blocks they needs to be unobtrusive, I used to hate a wide twist but now depending on the saddle I’m ok with it…

You may get more suggestions posting in the dressage forum…