I think I see where you are going here, have the real liquidity in the private sector where it does the most economic good, restrict it to the private marker to keep it from overfeeding, keep government lean and responsible.
Actually, the liquidity is more likely to come from the Blue Dollar. They will inherently always be in greater supply via
Gresham's Law. And will most likely be what most venture capital looses - why would I take risk's with Sound money? While the parity of the two will float and not be legally tied as Gresham's Law stipulates - but I will still expect the "sound money" to have a higher nominal value than the speculative supply. I would expect that most speculative actions will be taken with Blue dollars- and be contractually paid back in a combination of the two currencies commensurate to the risk. A low risk venture would probably demand a smaller percentage of "sound money' in return. A High Risk venture would be expected to pay back in a higher amount of "sound money" - and this will help keep the Blue Dollar in check with reality.
Private individuals and corporations could chose to do business in either currency, or both - Just like most Mexican street vendors price their wares in Pesos AND in Dollars, with Dollar payments being cheaper and preferred - like wise with Vendors who offer discounts for NOT using a credit card. People working for wages will probably require some set amount in Blue Dollars ( enough to pay federal tax) and demand the rest in National Bit Coin. Yes, the Feds can keep upping the amount of Blue Dollars demanded - and try to force more conversion of National Bit-Coin to Blue Dollars - basically creating an artificial demand for Blue Dollars- but the sound money is inherently more scarce- and in effect will simply add more value to bit coin if there aren't enough blue dollars readily available. Since the govt can only spend Bitcoin (except in a war) , the exchange rate just evens out for them, and there isn't any point. In a war, the govt can essentially pull on the value of Bitcoins, but in that circumstance, it should probably be allowed to. Of course doing so will just piss off the tax payer - and since they can essentially take out interest free loans in Blue Dollars, their path of least resistance will always be borrowing (printing)
Cash will be a momentary thing - you will "Withdraw" bitcoin as Blue Dollars ( as a system to print Bitcoin Cash is likely to become corrupted - just as TPTB print Gold Paper) -If you need "cash" you have it , but not as a long term store of wealth ( much like right now)
I think it could work.. or at least be better than what we have, but I admit its complicated, and there may be problems that need to be addressed that I haven't noticed.