The FX404 part should be right
FX would denote the fixed bridge
404 would denote the dual quad-rails
S would denote "Standard" (as opposed to "C" for "custom" for the maple top strikers)
X... who knows, they really made no sense of it. S/D was for the standard with a D-Tuna and headstocks could be reversed or normal but it seems like at some point they may have used SN for normal headstock orientation and SX for reversed headstock (but then they didn't do that for the beak headstock).
So yes, it does seem like your guitar would be an FX404SX
If there's any logic to the serial your guitar was made in '99. I have a 98 serial which has the beak headstock, skull tuners, floyd and only 22 frets. I think these weren't in production for very long and they went to the 24 fret banana headstock design pretty soon, for good reason. At some point they also went from a small medium jumbo fret size (found on my guitar) to jumbo frets (which everyone else seems to have)
As for the idea of it being made in 87... Yes, it does have the pyramid logo that was introduced in 1987 but it is definitely not from the pre-Gibson era of Kramers