I think this is a great way to explain the situation and present both the increased equity stake and the lower salary. Only addition I would make is that the day to day job will likely offer more ownership opportunities than a role that started at market rates.

Pre-seed Investor. Email: ash@sterlingroad.com. B2B, US only. I work with founders for 3 months before investing. More info: http://SterlingRoad.com/process

Pre-seed Investor. Email: ash@sterlingroad.com. B2B, US only. I work with founders for 3 months before investing. More info: http://SterlingRoad.com/process