I get the analogy to gold vs. gold-backed dollars, but in Bitcoin's case I can't think of any specific changes the Feds could make to a fork that would allow it to both (a) obviate almost everyone's need for Bitcoin and (b) be enough different from Bitcoin for the government to be satisfied with it (and hardcore bitcoiners to be dissatisfied with it).
Well one change they could make is to declare the fork is legal, while the original is illegal with significant +10 years jail time for using it.
It's not that different from simply declaring Bitcoin illegal. In either case the incentive to use Bitcoin is affected similarly, to the extent that FEDCoin lacks Bitcoin's key features. (And again, to the extent that it
doesn't lack Bitcoin's features, it's wonderful - just not for Bitcoin investors - but also highly unlikely to happen.)
More than that, banning Bitcoin and using a FEDCoin lacking many of Bitcoin's key features just hamstrings the US in the economic race. It's a giveaway to other countries.
Any fork could start out as an un-changeable supply. The FED's dollar was originally convertible to gold and thus had a fixed supply. Then during the next crisis they can default and fork again to increase the supply through default "for the common good".
This is a dream scenario for Bitcoin: they've familiarized the general public with some or most of the benefits of Bitcoin, now they are corrupting their own fork, driving people to use Bitcoin (or, if the original FEDCoin is sufficiently Bitcoin-like to keep people away from Bitcoin, then people will just keep using the more Bitcoin-like fork; if they also ban the original FEDCoin fork, then we're back to the "Bitcoin ban" scenario mentioned above).
So I can't see any move toward FEDCoin not helping Bitcoin, or at least advancing the cause of cryptoledgers.