I'll preface this with a disclaimer. I don't study economics, so my knowledge is based on some classical texts and some common sense. That said, Ron Paul doesn't study economics either, so we can be on equal footing here.
We ought to be very careful about listening too closely to Von Mises, champion of the Vienna School, without taking into account the last 50 years of economic thought. I'm not saying his ideas are bad, but the economy today is fundamentally very different than it was in his time, and we need to adjust our thinking accordingly.
As far as the fed regulating the money supply, I would argue that the amount of money in circulation is not arbitrary. If the government did, in fact, print up more money to cover its shortfall, then the economy would collapse. Clearly, fiat currency has to be managed smartly to avoid this pitfall. Whether or not we've been doing that is up for question, but even if we've been doing it wrong, that's not reason to throw out an entire system.
On the idea of competing currencies, I'm afraid I don't see the need. If you feel, right now, like your assets are deeply threatened because they're in fiat currency: buy gold. There's nothing stopping you. I'm not sure I understand why someone who wants to take the government out of as many things as possible would add a whole new governmental function of managing a separate gold-backed currency.
And as far as the Constitution goes, the founding fathers gave Congress power to coin money and set the value as it pleases (Art.1 Sec.8). The states have no such power, but that restriction is clearly limited to the states, as it's in with all of the other provisions that limit powers of the states (Art.1 Sec.10). Many of the prohibitions in that section are also separately prohibited to the federal government in previous sections (bills of attainder, etc.), but the restriction on what can be coined money is not one of them.