Riding mower stalls

I have a Simplicity Broadmoor riding mower, 14 hp Kohler Command engine. It starts (kind of hard) but runs good for 15-20 minutes, then sputters, and stops running. My understanding is that it runs out of available fuel. The fuel filter, situated right before the fuel pump is clear. When I first start it, the filter is full of fuel. After it’s running, the filter empties, seemingly faster than fuel can be replenished back into the filter. I have to let it sit for about 15 minutes, allowing the fuel to descend out of the tank and filter is full again. Starts, runs, then dies. New carb installed did not fix the problem. And recently I replaced the stock fuel hose with another run from the fuel tank opening down to filter, with no improvement. Please help!

Check for debris in fuel tank blocking passage.
Check impulse hose to fuel pump for leaks.
Pull off hose from carb and turn over motor to see if pump is pumping fuel from hose at a good rate.

When you say hard to start does the motor spin at a good speed?

I have looked into the tank for debris, but have not drained it enough to remove and thoroughly inspect. The metal pick up tube has a real small opening for fuel... I figured the 1/4” fuel hose dipped into the tank would allow any debris to pass. There are no leaks from tank to carb. Pump pumps fine. Is it possible it’s pumping more than it should, in turn “using” gas faster than it should? It runs good otherwise. There’s a rubber hose that runs from the air filter housing area up to the front of the engine, attaches to module looking thing. Is that some kind of vacuum hose? It’s pretty worn, but seems to do it’s job, whatever that is. As far as hard starting, it just doesn’t fire up right away. Speed is fine. Thanks for reaching out.

Remove blower housing top of engine & replace coil, gap clearance to .010 using business card between new coil & flywheel. Let us know how it goes, thanks, Mark

Disconnect the fuel line from the engine/pump, and hold it below the tank, allow it to flow into a container. Keep your eye on the flow and check it out. See if it slows, look at the fuel quality, if it starts slowing, loosen the cap, etc....

FWIW
o help understand what happens,
Grass clippings get into the fuel tank.
The fuel displaces the water in the clippings which are then only marginally heavier than the fuel so they float arouns in the tank.
As the fuel is drawn off they get dragged over the outlet & form a plug, like a piece of parer or leaves over a drain.
then when the mower stops they float away.
Nothing that is organic that gets into the fuel tank can decompose due lack of oxygen & water for the bacteria.
And while one can not lock off the fuel outlet over time you end up with a lot of them in there.