I'd have to wonder if the bevel gear & shaft are all one piece - It was fairly common with Ridgid/Ryobi which are the same tool as Milwaukee (Milwaukee is the "top of the line", Ridgid is mid-line and Ryobi the bottom end when it comes to the TTI brands - I used to be a warranty center for them... did lots of Ridgid stuff.) You say you sourced new bevel gears, did you actually get them in yet, and are you sure they're correct part number (Would need the full model and sometimes the serial number of the tool for parts lookup) Otherwise, appears to me to be a press fit gear which you'd need to pop the chuck off and bearing from other side, and then a hydraulic press with some heat (propane torch) to ease the gears off (Then to assemble , stick shaft in freezer for a few hours and soak the new gear in 120 degree hot oil and have to be quick and precise at getting the gear back on shaft in correct location... hence why I suspect OEM would be a shaft & bevel gear assembly)
Usually when the gears were meant to come off they were just a light friction fit, in my experience (and keyed in place - another clue to it being one piece is lack of keyway in the gear)