Yes, Tarev, giving the ball a little more sun may stem the leggy growth and choosing plants with less long and rigid stems (just look at the more mature sizes of succulents and that will tell you what they will look after awhile). As you mentioned, semps would be a good choice and look at some sedums that have softer stems that will grow longer and be pinned back into the ball to promote more root growth from their stem joints. This will help in spreading green covering over the ball. There's lots of sedum ground cover with little stem and some with just a little more stem that would work well with your ball. Think florist pins to anchor stems and foliage in place.
Yes, Semps and most Sedums thrive on a broader sun exposure. Here's a frame I just tweaked with adding small bits of sedum brevifolia held into frame with florist pins to help anchor as they root. This planting is combination of minimal stemmed plants, Echeveria and sempervivum.Hopefully in time it will fill in. Of course there's a lot more colors and textures out there to choose from that your huge ball can accommodate.
