I see what you are working with here! I've rehabilitated many critters, wild and domestic. So I see your pain, in the neck! Lol but since, I've had 2 children of my own. I got a baby carrier, to carry my kid on my back. (I do miles of hiking.) Well I found one I really like, that might be a good start for you. You could get some ideas on straps and such. I carried my kids till they was old enough to follow me, I wanna say my son was 30lbs last time I packed him. I have herniated disc and neck and shoulder problems. If you could take the straps off of it, and build like a mesh carrier on it. You would be set and ready for kitten carrying for days! Mine is similar to the one linked below. But I have put my moms small dog in it, he enjoyed it lol
https://ergobaby.com/baby-carrier/360-all-positions-baby-carrier-cool-air-mesh-sea-mist
Stitch in something like this!
https://www.chewy.com/jespet-soft-s...OuFUpG9fB8TbAmucqbZQ4Xn5Fdt1PJWBoCpkEQAvD_BwE