TK-380 2-tone
If you want a Kenwood that will do LTR and Conventional and be able to use the 2-tone feature you will need to step up to the replacement for the TK-380 which is the TK-3180. This is a much nicer and more user friendly radio and will allow you to do exactly what you want to do.
When you setup you radio you have the option to set the radio as conventional or trunking format. When you select trunking format, you loose the 2-tone ability. If you would set it as conventional, you will then have the option back. If you really need to keep your LTR system, then you'll have to upgrade to get the 2-tone option. Also note that on a Kenwood you cannot do 2-tone in a LTR bank either, on any of their radios.
Hope this all answers your questions.
Ambdrvr