Sounds familiar to me. Even though the tank gauges both read 3/4 full (mine is a 935 with 2 tanks), the suction lines in the tanks were split at the 3/4 level line. So, it would stall out after running out of fuel. Dropped the tank and replaced the suction line. In the process of sucking all that air, the electric fuel pump failed (sounded ok, just not getting any fuel pressure). Replaced the pump with one from O'Reilly Auto parts and everything is now working fine. Meanwhile, I've learned to carry an open-end 17mm wrench in the toolbox for cracking open one or two injectors in case I run out of fuel again. Since there are two tanks and two gauges, sometimes I monitor the wrong tank and get a surprise. The suction line was not fuel line, but some kind of yellow brittle plastic that disintegrated when I pulled it out.
Not that hard to drop the tank. Pull out the sender and you will have the suction line coming with it. There was water, dirt, wax and tree leaves in my tank. Save the inlet screen and reuse it. If your suction line has broken off, fish out the screen.