I'm also curious what "direct supervision" means in the legal sense. It implies that your CFI has volunteered to be in the crosshairs for any and all scenarios involving a claim. From my experience doing primary training the upside is you might cover expenses. Of course the downside is huge..... I think the most realistic approach may be to get the license taken care of with a rental then go to the kitfox insurance application with a more attractive history. I think you will find that buying the airplane is probably the easiest of all the activities involved with owning and flying in the AM/EXP category.