This is interesting. I hadn't thought of the role of inflation as an incentive for groups to be careful with their membership. I don't think it applies in this case, though, since the total number of members in any given group is the same whether they are honest or pursue this scheme (one account per group). It would certainly cause inflation in the system as a whole, but it doesn't directly cause inflation in any particular group's currency. (I think.)
Verifying that Martin Koeppelmann is a real person and has not already joined our group, while it has its own challenges, seems much easier than verifying all of those things and also verifying that there is no other instance of Martin Koepelmann in any other group. It seems like doing this sort of verification might require a lot of cooperation between groups.
Out of curiosity, how do you see the group distribution in the final state of the system playing out if it is successful? Personal connections are viable up to a certain group size; do you see most of the value held by individuals being in the form of small-group coins?
This is an interesting answer, and it's a layer I had not considered. I wonder if there is a metric for this that is sufficiently hard to game.
This is interesting. A transaction fee is nice in that it encourages a more densely connected graph; in fact, just the presence of a fee might eliminate the need for the trustee bonus, since longer trust chains are more costly to traverse. But I'm not sure it provides a big incentive for individuals to stay liquid. If I understand correctly, the consequences of trusting a bad actor can include basically losing all of my liquid assets; that's a very big risk to run if I can avoid it.
More generally, have you thought about trying to prove (mathematically) some properties of the proposed system? Having some provable guarantees out there would lower the fear that there is some clever way to cheat the system.