This still seems off to me. If I were a potential creditor in such a closed loop system, and I was told I absolutely could not charge interest due to these monetary supply constraints, I would either just stop lending entirely or I would demand something that isn't strictly denominated in money to make the risk I'm taking on, etc worth my capital outlay.
But then eventually, if the system were sufficiently complex, I'd probably tire of whatever complicated barter system we have already going on, and then it's likely some third party would step in offering something that's totally not money, dude, trust me, it's just like a handy clearinghouse of IOUs for people engaged in the trade of these non-monetary favors for favors...
Some people who hold or offer such IOUs might then take the bold step of calling them non-exclusive, as in I will mow the lawn of whoever happens to have my "one lawn mowed" voucher, I just happened to originally give it to this first guy, I have no idea what he did with it after that... Other people realize this "non exclusivity" deal actually makes the voucher strictly more valuable, you can do more things with it than you could otherwise... You see where I'm going with this. It's not passing my sniff test.