I'm excited to see the results of everyone's projects!
A few thoughts: There already is a peach cultivar with an edible kernel, like an almond. I think it's grown in India.
Different ploidy levels are a barrier between Prunus species, but blueberry breeders have similar ploidy issues that they've overcome in various interesting ways. There are many different species of blueberries at various ploidy levels, diploid (various wild species), tetraploid (northern and southern highbush), and hexaploid (rabbiteye.) People have crossed diploid x tetraploid to get a sterile triploid, which they then doubled with colchicine to get a hexaploid to cross with rabbiteyes. They've also crossed diploid x hexaploid to get a tetraploid to cross with highbush.
It would be cool if it were possible to cross some of the really sugary Prunus species, like European plum (hexaploid) with peach, sweet cherry, or apricot (diploid) to get some sort of sugary tetraploid, which could be crossed with tetraploids like the Romance series cherries to get something both sugary and cold-hardy. This wouldn't require any colchicine. Of course, there may be barriers besides ploidy between these species.
The time it takes to grow seeds might be a barrier. Considering that sweet cherry or apricot seeds develop very fast in those early-ripening fruit, and other fruits like late peaches or plums have slower-developing seeds, I don't know if hybridized seeds would develop properly in the time it takes for a fruit to ripen. Zaiger genetics sometimes uses techniques like embryo rescue to overcome this incompatibility, but this is probably beyond the reach of the typical hobbyist.