One issue with phantoms (which I believe the above linked to gun had issues with) is the breech drop design. The area the ball, or in this case round, enters is larger in size than the barrel. So you have the push the round up over the lip. Not too big a deal with a round ball, but the bullet shaped FS round with a fairly fragile skirt could have some issues.
And remember, the skirts on FS rounds are hollow, so if you tried to put them in a normal spring feed they'd nest together.
I did fab up a rough prototype of a horizontal First Strike spring feed. Ran out of scrap material at work so I could never finish working out the bugs...
Of course this layout would have to go forward from the feed.