Wadman,I'm not familiar with the 773,so the "grommet" thing may be the problem.
I had a similiar problem that slowly got worse with my Bobcat.After sitting a few days it would fire right up,but then die after about 2 seconds.Then it was VERY hard to get restarted again.If it had just been running awhile,it would fire right up,and wouldn't stall at all.As time went on it was harder and harder to get started cold.It acted like air in the lines,but it turned out to be the injection pump.It was just plain worn out.There was too much clearance between the close fitting parts.
Hopefully that is not your problem,the pumps are expensive.If you truly have air in your lines then it probly isn't the problem.I've a Isuzu 2AA1 diesel in mine.In mine the fuel is drawn up the fuel line,out of the top of the tank,it then goes into a seperate mechanical lift pump,then it's pushed through the filter assembly,and finally into the injection pump.Mine doesn't have a grommet in the fuel tank,other than the one sealing the fuel/fuel return lines, where they enter the tank(and they couldn't cause a starting problem).I'm not sure why yours would have a grommet inside the tank either,but it may have one regardless.
If fuel level affects this problem,then it probly is inside the fuel tank.A fuel line leak between the tank and engine would most likely show up with diesel fuel leaking out also.Without any signs of that,I'd next look for anything that could restrict fuel flow(pinched line,plugged filter)or possibly a defective fuel pump(if it has a seperate one).My lift pump has a lever mounted to it too manually operate it.If air is in it,it feels mushy when moved,and firm when the system hasn't any air.
I know it's not specific info for your model,but maybe it'll help anyway.