For those interested in creating a fertile cross between raspberries and strawberries my educated opinion would be that one should use octoploid Fragaria ×ananasa as the seed parent and find a tetraploid Rubus idaeus to use as the pollen parent.
The most likely result for offspring would then be hexaploid with two sets of raspberry chromosomes that can pair wth eachother along with four sets of strawberry chromosomes that can pair with eachother. These resulting plants could then potentially be fertile enough to bear fruit themselves.