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It looks like you are a making simple thing complicated. The test circuit in post #3 with it's accompanying waveforms is bringing all necessary informations for a practioneer. It's rarely necessary to do much calculations, e.g. to know if the exact oscillation frequency is 1.3 or 1.4 kHz. Otherwise, you should probably refer to better defined devices than UJT.
I agree, that UJT, are perfect for some kinds of low part count circuits, e.g. to drive a triac or SCR through a trigger transformer. I have used them previously for similar purposes and have still some in a component drawer. But they are simple parts. Put them in a basic oscillator circuit and they either work or not.
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