the 303 cleaner is very good on some materials if very un-fresh, we used the product on the sunbrella poptop fabric before reapplying the protectant, just test in an area out of sight first..
steam can work just depends on level on un-freshness, may take a few days of mopping, an needs to be tried in un seen area first,
I use the carpet head and carpet slider rather than the hand attachment on our seats but we don't have suede fabric
we use ours just to ensure house dust mite and the like are exterminated