There is no sediment. There is nothing in the old or the new fuel filter. The gas tank is also made of plastic. No rust. No anything else. The fuel filter is new and clear plastic, gas is passing clear and clean.
Just so you have this clear in your head, and it might not be a contributing factor.
Grass clippings end up in the fuel tanks of most mowers along with all sorts of other strange things.
The fuel displaces the water in the clippings so they sort of float in the fuel , not on top of it, much like alge scum in a bottle of water.
When fuel is being drawn out of the tank they get dragged to the outlet by the current in the tank where they can form a plug.
Come tanks are known for having a casting fin which partially blocks the outlet & snags all of the floaties passing by it, Cubs are notorious for it.
This can take anywhere from 15 minutes to several hours.
Because they do not pass through the tank outlet, they do not end up in the filter.
When the engine stops, there is no flow so they float off and disperse sort of evenly in the tank again.
So after a 1/2 hour or so enough of them have dispersed to allow full fuel flow & the mower starts right up & runs like a pearler.
Two tests for this
1) the instant the mower cuts out whip off the fuel line from the tank, before the filter or pump and blow back through it as the previous poster mentioned with his rust clogging tank.
IF the mower starts back up right away in place of waiting the 1/2 hour or whatever is the normal recovery time then a plug becomes prime suspect
2) use a auxiliary fuel tank either for the whole mow or plug it in the instant the engine stops.
Remember you are there describing what is happening in words.
We have nothing to go on but those words
People use different words to mean the same thing and the same words to mean different things , they often overlook things that tech would pick up on if we were there looking at your mower & drinking your beer.
Every tech can tell the difference between an electrical stall & a fuel stall by the actual sounds the mower makes and the sequence of those sounds.
Like a lot of things, mower repair is the art of eliminating what the problem is not rather than waving a magic wand and pronouncing what the problem is.
There are very few instances where a single set of symptoms define a specific problem and in many cases the actual problem can & does have several problems at its root cause.
Now you have a problem that you have not encountered before so you don't understand what is happening.
We are all trying to assist you and any one else who chances upon this thread with a similar set of symptoms.
You might also like to take note that no one has fobbed you off with a "change this part " as if we are the Gods of small engine repairs.
We have simply asked you to do some investigating and get back to us with the results.
If we were there we would have recognised that the valve lashes were way out of spec by the way the engine starts and the sounds it makes running.
You may or may not have a plug but we do not know that until it has been checked.
If your problem was nothing more than the valve lash they lucky you just try to remember to check them every couple of seasons.