The June 2021 rejection of the Swiss CO2 law leaves the Swiss Net Zero strategy highly uncertain. We develop and analyze a new approach based on fully funding future required CO2 removal, using biological and geological means. 100% of Swiss territorial emissions would be removed in Switzerland, and all embodied emissions of imports in the region where they were emitted, to ensure compatibility with the future European carbon border adjustment mechanism. The project covers (1) Establishing new responsibilities and principles of Swiss climate action once the global 1.5°C budget is exhausted, likely by end 2027, (2) Preparing the creation of a Climate Cleanup Fund to effectively finance removal of CO2 in excess of the remaining carbon budget, for these emissions replacing all current instruments (ETS, CO2 levy, KliK), and (3) Setting up a pilot project, at the scale of 0.1% to 1% of the Climate Cleanup Fund depending on number of participating organizations, to test and refine all aspects of funding, project selection, accounting, governance, and communication.