If Zimbabwe adding extra zeros before the decimal point to its money doesn't cure inflation, then Bitcoin adding extra zeros after the decimal point won't cure deflation.

Inflation killed the Zimbabwe currency because delusion caused it to become worthless not because of availability or velocity issues that people are worried about in Bitcoin. These are two separate issues that people always seem to talk past each other on the subject of Bitcoin deflation. Splitting a Bitcoin into smaller units allows for unrestricted availability and velocity. Anyone can always buy and sell at market rates to complete a transaction. Inflation or Deflation of the currency has no effect on its availability. So why is it bad if it is deflationary?

Zimbabwe was very different: the amount of money people had was devalued by new notes being printed that had extra zeroes before the decimal point.

Adding extra zeroes after the decimal point for money already in circulation leaves the total supply the 'same' but could also be viewed as increasing supply 10-fold, without disadvantaging anyone currently holding the currency.

Its never happened before, so I'm not sure many economists have thought about it

Changing denominators has an effect on the liquidity of small transactions, but it's not going to change inflation.

What inflation does in an economic sense is much bigger - it changes who has relatively more or less wealth or debt over time. If you take out a loan for $10,000 and inflation makes both your prices and wages go up 2x, then you now have half as much debt.

Deflation does the opposite and makes debt more and more expensive. This is why most economists are against it - debts that grow more expensive will trap people. Historically, debts were forgiven by decree (a jubilee) because the system kept breaking.

To me this is one of the most interesting things about Bitcoin. It is an asset based currency. In a debt based fractional reserve dollar economy you or someone else owes that currency back with interest. The economy is like a game of musical chairs. If a society was based on something like Bitcoin everyone could have assets, there wouldn't be as a strong need to borrow as there is today.

If Bitcoin was a predominant part of an economy borrowing a loan in it could be very bad. In a predominantly Bitcoin based economy everyone could have abundant wealth and there would be no need to be a debt slave.

If the US government started minting 0.1 cent coins and 0.01 cent coins, would that be viewed as increasing the supply of dollars?

In Bitcoin the supply and availability of currency are decoupled. By funging or splitting a unit of Bitcoin currency into pieces you increase the availability for use while preserving the value of everyones holdings. Based on the supply and demand the price will fluctuate independently of supply levels.

My understanding is that regardless of how inflationary or deflationary Bitcoin is, there will be no effect on the availability for anyone to buy and sell.

If the USD was deflationary, then maybe it would?