The only time I’ve had a problem cleaning spoked GS/GSA wheels, is when I used Muc Off. This left a white coating on the black rim, which was a bugger to get off. Ended up scrubbing them with WD40. Since then, I only use a PH neutral shampoo on the bike, such as Auto Glym. Use this with a proper spoke wheel brush and they take no longer than an alloy wheel to clean. And spoked wheels just look so much better!
Muc off is fine - but never let it dry - soak the wheels - apply muc off - watch and wet as required brush scrub rinse.........simple - never let any cleaning product dry out