They've done the general flat pickup rout and then done the extra rout for the humbucker pickup legs, without then tidying up the remaining wood. I'd definitely remove it as it serves no purpose and removing it helps with cable routing.
However you might want to fill those extra leg holes if you plan to direct mount the pickup to the body. There is very little depth of wood between the bottom of those routs and the trem cavity, and I wouldn't like to use really small screws to hold the pickup in place.
Not quite sure why they've also routed similar leg holes in the single coil routs. They don't look wide enough to fit Gibson-style mini-humbuckers in. The mini-humbuckers from my Firebird are 27mm across and the mounting legs are really short with about 2mm depth to them so wouldn't need the extra routs.
I don't think you'd need to do any particularly special routing for a Floyd Special. On the GST-1 Hexacaster, the 2-point trem had the same bottom of plate depth to top of saddle dimensions as the Floyd has (10mm according to the Floyd dimension pdf) and I got that floating without the need for a shim. I did fit a shim at first, but then removed it as unnecessary. The GSR-1 should have identical body/neck dimensions. I did file down the ends of the post inserts so they didn't stick through into the trem cavity, but that was about it.
You can always use a mini-toggle switch for pickup selection, which is less obtrusive than a full-sized toggle or lever switch. Or you could a rotary switch and have two knobs instead of one. If you didn't want a blower switch, you could use that as the pickup selector, or if you didn't want a mixed pickup position but just neck or bridge, then a mini-toggle with more poles could probably act as a bridge/neck/blower selector.
Or even fit a 3-way lever switch but don't put a toggle on the end, and round over the edges so it's more comfortable to use. That wouldn't be too obtrusive, especially from a distance.