I don't think you would ever use a side float to cut the abutments. You use an edge float or a saw.
On any double iron plane, the line of the abutment, if continued down, will always hit the wear. On a single iron plane, that line will more or less coincide with the front of the mouth, so when you add in another 1/8" or so for the cap iron, the abutment
has to be forward of the mouth. So, you're always making a stopped cut on a double iron, whereas on a single iron you can just run the saw right through the mouth.
My favorite tool for cutting the abutments is an old drywall saw, with all the set removed and the teeth reshaped for cutting wood. It cost me zero yankee dollars.