We might have a paradigm issue here, but I'd say bite the bullet and accept hyperbolic discounting. Lack of transitivity is just an artifact, and not a problem in the real world. There is an essential difference between cases where you can change your mind and cases where you cannot.

Here's a simple example. I'm claiming this is extremely typical, and scenarios under which exponential discounting arises are very much not.

When you lend some money to someone for 30 days you should charge interest at rate P. Due to some combination of opportunity cost and risk of the borrower running away with your money or dying and not being able to pay back etc.

When you lend for 60 days instead, the risk of bad things happening between days 31 and 60 is much less than between days 1 and 30. If the borrower wanted to run away, he would. If he survived the first 30 days, it's a proof that his lifestyle is probably not that dangerous, so he's more likely to survive the next 30. This decreases the rate to P' < P. (the same applied to opportunity costs before modern economy). Exactly as hyperbolic discounting predicts.

When you lend to one person for 30 days, and another for next 30 days, your proper interest rate due to risk is back to P. But this is completely different situation, and much less likely to be relevant. And in any case systemic risks of staying in business get lower with time, what should gradually reduce your P.

Usually the points of time where you can "change your mind" correspond to events which introduce all the new kinds of risks and transaction costs and are not neutral.

I'll understand if due to paradigm mismatch you will have hostile reaction towards this.