Landing performance of almost all light jets on a wet runway negates contemplating use of 1000m the vast majority of the time. Often the smaller ones have very poor landing performance but adequate take-off capability. Absolutely forget the likes of the Premier 1, Beechjet, Hondajet, Phenom 100 etc. Even the 'baby' jets like the Eclipse and Vision SF50 have the Achilles heel of inadequate stopping performance on a wet runway. Often some of the larger types have better field performance actually. The Phenom 300 is notably better than the 100 for instance. Stick with the very smallest straight-wing Citations in this context, albeit some can't make the 1,200nm range requirement. Often the older ones are actually better than the new versions.
I'd forget a jet and go for a King Air or PC-XII. For the King Air, go for some of the aftermarket mods available - Raisbeck etc.