If you're just trying for a profitable trade there is no big reason to have the puts against the same ticker as your long position.
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My reason for that is simple: You!
Your discovery of the quite reliable relatively narrow Price/Peak BV band in which Berkshire trades.

Fair enough. But if you merely want to make a buck from puts when things go south, you probably want an asset whose price does NOT tend to stay in such a narrow band!

Ideally it would be something that is wildly overpriced now on as many metrics as you can think of, and preferably has good odds of being underpriced in a panic--its holders are the types that would bail in panic. Some of those will usually be found among as-yet-profitless high growth companies, especially smaller ones that are not #1 or #2 in their fields. Sometimes they don't hold up well when the growth metrics stumble.

Good rules of thumb for any short-like position: never more than notional 15% of your portfolio, and heavily diversified. The Karenina effect: good companies are all good in the same way, but every company with problems is problematic in its own way. They are inherently a very much less predictable group than good companies.

And most market tops aren't sudden. There is no hurry to enter your shorts. You can probably wait till serious cracks have appeared--months since the last market high--and still make lots of money as things fall in price.

Jim