Ich schloß die Tür leise, um das Baby nicht zu wecken.

[cazort]

I notice another exercise has the same form of this verb but spells it “schloss”. Based on its pronounciation (short vowel) and the recent spelling reform, I think that this spelling is probably archaic. Is that correct?

If so, it might be good to either remove this, or notate it somehow. I have noticed that there are a few other archaic words included, perhaps because they are common enough that you would encounter them, but it seems important to note that they are the old spelling.

[dlobok]

Yes, schloß is archaic.
There is, however, a certain group of people who seem to be absolutely incapable of accepting that language reform from almost 30 years ago, apparently also on Tatoeba