It's possible that if you found a new TV that actually has a sleep timer function (not just a power off after X hours of no usage) you might be able to use an older remote for that brand that has a sleep button on it.
I have an older Samsung and a newer Samsung and the old hundred buttons remote works perfectly fine on my newer Samsung.
Unfortunately there's no sleep timer button, nor sleep timer on the newer Samsung so I can't do you a test run but with some sleuthing you could probably find the right brand to do this with.
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