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A lot of good ideas coming here to help me. Next step is getting the telco guy to install the DSL switch.
Why the DSL switch? If you are going to backfeed from the OBI to the kitchen phone using an unused pair, i.e. black-yellow, you are not on the telco line at all. That would be only if you are getting rid of telco voice completely and going ONLY with VOIP. If you are keeping telco voice on the kitchen phone, why do you need to make any wiring changes at all?
Note: the pairs are not going to be red-green and black-yellow if you are using Cat 5 or 6. They use a totally different color code than in the ancient days. That's just a side note because it is easier to talk about red-green, etc since so many people know what that means.
So, do you want the kitchen phone on VOIP or on telco voice? The wiring is quite a bit different depending on that choice. Knowing that will make the recomendations much easier than speculating or trying to cover multiple senarios.