ive used imperial cleaner on my table about 5 times now, i havent used quik-clean, but i assume theres no difference since it cleans really well.
after vacuuming, instead of spraying directly onto the table, i spray the foam onto an old t-shirt, dissolve the foam into the shirt and gently wipe the felt down with the wet rag(i was told to "dab" the felt, but it didnt seem to pick as much dirt/chalk up). it really suprised me the firt time i used it, it was pulling out dirt and chalk from years ago, and took a couple rags to get the job done. like i said ive used it about 5 times and theres hardly any chalk or dirt coming out anymore. after cleaning i vacuum a quick second time.
if you havent used it before i suggest spraying some on a clean cotton cloth rag or t-shirt and trying it under a rail or a conspicuous area.