Welcome to the world of the 280C. They are quite a bit of fun to drive and relatively easy to get parts for, with a few exceptions. The M110 has a few weaknesses that I will mention here, maybe this will be of some use either now, or somewhere down the road. It uses a transistorized ignition module and points. They are a disaster.
The ignition modules used to be reliable from what I understand, but I think they are past their prime, expensive to buy, and expensive to have rebuilt. My 280C, a 1974, must have broken down on me twenty times before I gave up on trying to make that system work. The symptom was sudden complete loss of spark without warning. I went to vintage performance (retro-rockets) and spent $104 on a flamethrower coil and a Pertronix ignitor module. This got rid of the ignition points, the original coil (mine failed as well), AND that ignition module. The installation takes all of thirty minutes, and gets rid of a bunch of no-spark variables. It has not failed since.
I have not seen a fuel related issue particular to this car that caused it not to start. I HAVE seen plenty of fuel related issues that make it run awful. Overtightening of the four carburetor mounting bolts, causing nternal vacuum leaks within the carb is a biggie. I am not saying that your problem is not fuel related, of course. Typical fuel supply issues can occur, but I just can't think of any that are typical to this one car that don't apply to any carbureted beast, aside from over-tightening the bolts, which will make it run bad, not fail to start.
The cams are a weakness. Too many cam bearings to be oiled, not enough oil supply to go around. It leads to the cam lobes and followers being eaten for lunch. The replacement camshafts have two less bearings per shaft, increasing the oil flow to the remaining bearings, as well as the rockers and lobes. The unused bearing oil holes are to be plugged with set screws when the camshafts are upgraded. It is a real pain of a job, but I did it, and if I can do it, anyone can. Keep the coolant in good condition. coolant that has lost its ability to control erosion will eat away at the narrow walls in the head that keep the coolant passages and cylinder combustion chambers, and oil passages apart. In perfect condition, these walls are only about 5-7mm wide, so it doesn't take much.
Clean out behind the front wheels. There is a recess in there, behind that metal panel. Dirt collects and holds in moisture, and clogs the drain holes. This causes rust in the front fender bottoms, as well as the fronts of the tops of the rockers. I clean out these spaces in all of my 114, 115, 108 etc. cars. If there is already any rust in there, take care of it now. When buttoning things back up, throw away the two screws that pin down the bottom of the front fender (located behind the chrome rocker trim strip), and replace them with the same size STAINLESS screws. This eliminates much of the future corrosion problems, and makes them easy to remove in the future, if necessary.