Sloof meaning an apron comes from the Middle Dutch slove/sloof (an apron with short sleeves) [source].
Sloof meaning a drudge or toiling housewife comes from the verb sloven (to work hard, to drudge, to show off). For example, Hij haat me en ik sloof me uit = He hates me and I’m slaving for him [source].
A sloof (drudge) might wear a sloof (apron) and sloffen (slippers) as they slip (slip) around their sloffige (dusty) house seeking a sloop (pillowcase) and trying to avoid a slop (bad situation) and trying not to fall in slaap (asleep).
There are probably plenty of other words beginning with the pleasing combination sl in Dutch – there are certainly plenty in English – slip, slap, slop, sloop (from the Dutch sloep), slide, sleep, and so on.
The English word sloven [ˈslʌvən] means a habitually dirty or untidy man or boy; a low, base, lewd person, and used to mean an immoral woman. It comes from the Middle Flemish sloovin (a scold), from the Proto-Germanic *slup-. It’s related to Middle Dutch sloef (untidy, shabby) [source].