The President will be equal before the law, and will not be protected by Sovereign Immunity. The President will not be constitutionally linked to any faith.
Investigate the feasibility of direct digital democracy - using online tools to gradually replace representative democracy with increased direct participation in the legislative process by all electors.
Investigate methods for deliberative democracy[^3] - things which increase research and understanding before decision making. Run trials of these for small decisions. Implement proven ones for members of the upper and lower house, and for ministers.
[^1]: Do we need a written constitution? - The Constitution Society
[^2]: Campaign against royal secrecy [^3]: Rebooting Democracy: A Citizen's Guide to Reinventing Politics - Manuel Arriaga