Hello! Here's a small-footprint 8x8 (8-input, 8-output) belt balancer design I just threw together!
8 inputs (fully balanced)
8 outputs (fully balanced)
Unlimited throughput
All belt types
Low footprint (76 tiles: 8x9 + 2x2)
(Passed cursory brute-force testing of input and output balancing and throughputs. Theoretically optimal, more testing may be required to verify this. Please let me know if you find any issues.)
Nice! The topology checks out for a balancer, and it has the same area (76 tiles) as the one in Raynquist's balancer book (you can easily move the two outer splitters one tile down). Unfortunately, with the two undergrounds sticking out yours is one tile longer. (I mention this mainly because I first thought yours was smaller.)
Also you say the balancer has "unlimited throughput", but this is only when all the inputs and outputs are being used, so it is not throughput unlimited (TU). A splitter network is TU when it does not limit throughput for any combination of input and output belts. For that an 8-8 balancer needs at least 12+(12-4)=20 splitters.