You're absolutely right that the Crosscheck is not a true cross bike (the presence of mudguard eyes and bottle cage bosses) gives that away, but it is not dissimilar to the Karate Monkey, Roadrat or Kaffenback you originally mentioned (i.e. pretty versatile frames) none of which are cross frames either.
If it's for a mainly road commute with occassional offroad action then I'd have thought any of these would suit, if it's for a lot of offroad or even cross races then a dedicated cross frame would be more suitable or possibly the Karate Monkey of the original selection.
If it's for a mainly road commute with occassional offroad action then I'd have thought any of these would suit, if it's for a lot of offroad or even cross races then a dedicated cross frame would be more suitable or possibly the Karate Monkey of the original selection.