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In an attempt to cut down on the whipsaws, I investigated only doing a switch if the difference in returns was greater than 1 BP (0.01% absolute difference).

If you're using market at close orders, the trading costs are limited to your commissions only, so it should be very small as a percentage of the trade.
In that case, trades are to be avoided primarily for the reason of hassle, and that it might actually make the thing work better.

For trading costs under (say) 0.15% of trade value, as they should be, a quick test of my three-way system seems to show it works a bit *better* by reducing trades.
e.g., compare the returns on what you've been holding this past month to the best performing of the three;
switch only if the best performing outperformed you by at least 35bp (0.35%) in the last month.
Even with no trading friction this backtests with slightly higher returns than switching willy-nilly to the recent best.
The advantage might or might not hold, but it certainly seems to show that there is no obvious penalty being a bit hesitant to switch.
The three-way strategy has more trades per year than the two-way strategy, but this reduces it from 7.7/year to 5.7/year.

This was a kind of "quickie" test so don't take that result as gospel, try it yourself.

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