Even in its hardware form, 1988's Kawai K1 - often viewed as decidedly low-budget alternative to Roland’s all-conquering D-50 - was more ROMpler than full-on synth, being a collection of multisampled instruments with relatively few hands-on editing options. So, it stands to reason that a software plugin version should be pretty authentic.
Nils Schneider’s K1v is precisely that, and the good news is that you can download it for free.
This promises to accurately emulate the K1’s 8-bit synthesis engine and parameters, and includes 768 presets (that’s the factory bank and all the ROM cards). You can import and export SysEx presets and banks to/from the original keyboard, and you can also use the K1v as a software editor for said hardware.
As things stand, K1v only runs on Windows as a VST2 plugin, but Mac and Linux support is said to be coming.
You can download K1v for free from the Nils Schneider website; be sure to support the developer by donating if you like it.