Hi demiskeleton! Great that you like the game.
A physical copy of BDC, such a good idea!
There is no other way to get clovers, their goal is to give bonuses to new players and encourage them to try different strategies of upgrading. At some point you will get no more (unless you complete all the objectives on the clover's list, which is impossible in the demo).
But don't worry, it's normal to lose often before reaching the epilogue of the game (it's a kind of "die and retry"); you'll need to be strategic and lucky!