Hi Head-Case, great forum you guys got going on here. Much more straight to the point than some other major headphone forum(s), makes finding proper information easier.
Replying to the OP: The closed pair of headphones that to me resembles K1000 the most, is the W5000. Similar speed, similar detail, similar soundstage. Less bass, closed and somewhat coloured (sweet, toe-tapping euphonics) in the midrange though. The W5000 also has the positive aspect of needing much less amping, unless your mother wants to throw huge amounts of dollars on upstream components. Both of these are very revealing though, so a good source is a must.