There is an alternative: use unemployment (some vector or indicators not just U3) to target the "unemployment" portion of the Fed's mandate and the Price level to target the "price stability" portion.
Under this approach the Fed would goose inflation (with interest rate changes, QE in LT government backed securities, private securities, exchange rate intervention, whatever instrument it chooses) as long as their forecast for the price level remains below target.
The Fed would try to rein in inflation (again, with whatever instruments) when the price level was above target unless the unemployment vector was also above target. What ought to go into the unemployment vector, how to make the price level forecast, and which instruments to use, what level of unemployment to target and what rate of change of the price level to set as the target would remain matters of "Fischerian" discretion.
I think that's a pretty good description of what I would call "dovish bias" in policy. Lots of people think that way. If you look closely, however, the policy is not symmetrical. He calls for "reining in" high price levels as long as unemployment is not high, but then calls for boosting low price levels without any reference to the unemployment rate. His proposal will be asymmetrical, and hence destabilizing. To make it symmetrical, the Fed would need to refrain from boosting a low price level if unemployment is also low.
Under his proposal, the Fed would probably find itself refraining from slowing down excessively fast NGDP growth as long as inflation was not high. This would lead to labor market overheating, and an eventual relapse into recession.