Separation of 1) power to propose and draft bills and 2) power to decide on bills
Parliamentary representative system would be no real improvement, as it was parliamentary representative system that Iceland etc. revolted against. All new democratic constitutions in various countries have steps towards more direct, participative and horizontal democratic systems. Also in parliamentary systems the system becomes corrupted by partisan politics, party hierarchies and moneyed interests, as partisan governments hold both administrative and legislative power.
The solution to this problem which I propose goes like this:
1) Power to propose and draft bills belong to all citizens (citizens initiatives), but for everyday governance there is representative body of experts from various fields who negotiate and discuss and propose bills. It has no power to make any actual decisions, just to draft and propose, as a body of elected bureaucrats. We could call that body "Parliament" as it's function is to talk and negotiate.
2) Power to decide - accept or reject bills proposed by Parliament - belongs to either Citizens Assemblies (on small scale local communities) or statistically representative body of citizens who are not elected but selected by lottery - cf. juries. Reason for this is that direct democracy referendums over all proposed bills would be too tiresome and difficult to organize on more larger and complex levels of social organization. Proposals to change or amend constitution would always require referendum, perhaps with some qualified majority. We could call this body "Congress". It would not have to convene physically as it could work also through Internet and/or specifically designed Intranet.
This the idea in most rudimentary form with lots of details to fill and open to discussion.