Once the interest rate hits its maximum allowed rate, the size of the basket the BIC is pegged to will adjust downward until a peg is achieved. The downward adjustment in the BIC would remain as the new baseline. This is a one-way downward latch.
This is a fatal flaw. You're describing an inflationary currency, since over time it will end up having less and less purchasing power.
I don't think this is a very good idea.
RE: Hypothetical Price Stable Crypto Currency with Basic Income