I don't understand how this is supposed to work. If you have multiple Digital Promissory Notes backed by the same bitcoins, what happens when someone redeems one of the Digital Promissory Notes for its bitcoins? Then the others aren't backed anything anymore, so you've got the same problem. Fractional reserve banking always relies on trust: the depositors have to trust that the bank won't make unnecessarily risky loans with their money, and the bank has to trust its debtors to pay back their loans on time. There is fundamentally no way to create debt-based money without trust.
On a 50% reserve ratio there will 50% of the deposited bitcoins available as "demand money" on a day to day basis. As with the current system, if everyone demands all of their notes to be redeemed at once then you have a problem but the supposition in an fractional reserve system is that not everyone will do that at once. If the issuer of the note over extended itself or made bad investment decisions then depositors lose faith and you get a bank run whereby investors will lose some or all of their deposits. DPN's would be fungible with other Savings & Loans pools as long as the notes have the same reserve ratio as that pool would also have, in this case, 50% of their deposits as reserves available as "demand money".
In the past an old school goldsmith could just get greedy and issue more and more notes against his deposits. It has been that inability to trust lenders not to do so in the past that has lead to the extremes of economic expansion and contraction. If a paper bank note could notify you that its issuer is being a bit sneaky and issuing loads more notes against the same gold deposits you'd be alerted to the fact that and go and demand your gold deposit back asap. But it can't.
A network managed system would help prevent this. You'd still have risk in the system - but risk is either rewarded with interest payments on your loans or punished by too many defaults on your loan pool. However, the issuance of notes would not be abused as any holder of a note would know what is is backed by in real time. The community would decide en mass what is a safe level reserve to be held against the notes that they are willing to use as a means of exchange at any given time rather than an centralised authority.
This would allow for economic expansion but only up to a point that the whole Bitcoin community decides is safe. Real market forces would drive expansion and contraction rather than relying on the manipulated centrally controlled system that we have today which has proven itself to be so damaging.
If over time the economy starts to contract, either loans will be repaid and notes removed from circulation as the money supply decreases or else loans will default and investors will wear losses as they should in a free capital market economy. Rewarded for sensible risk with interest payments in good times. Punished for excessive and poorly managed risk in bad times.