Dave - Don't be that guy that just starts replacing random parts, lets troubleshoot this thing.
Easy stuff first; the tank screens are just bad, they clog easily and you can't really tell just by looking in. When the tank gets low again siphon into a clear container so you can let it settle and see if you had water. With the tank siphoned out you can pull the fitting out of the bottom of the tank. Inspect the screen for clogging, but even if not clogged I would snip off the screen. Then move upstream and put a small inline disposable fuel filter in. Kohler and others sell some nice small ones that are about the size of a golf ball which will hold much more dirt then you will ever let in.
Also, when the problem happens, stop at the exact spot it occurs at and shine a light into the tank and be sure the outlet is still covered with gas. Also with it still running pull the side panel and make sure you don't have any collapsed or soft fuel lines, but not likely, as it only happens when tank is low.
After all that checks out, then you can suspect the fuel pump.
As far as clogging of tank outlets go, I even had crap block the outlet of a Cyclops tank which doesn't even have a screen! I blew compressed air back through the line to break up the clog. It doesn't take much to clog up those little fittings. The screens are way worse.
Just don't be the random parts replacing monkey, you can do better!
. Mine r with the 2072. Last night i was mowing and.... yes just thinking how trouble free this tractor has been. Before every mow i fill up the tank and check the oil. So im mowing and it starting to get dark and im pushing it pretty good to get done without needing the headlights for too long. At this point i have been mowing for about two hours when i notice an intermittent stumble in power. Then i notice it again and again. Not enough to stop.....nothing was going to stop me when i have about 5 minutes left. Then i realize it seems to b while moving up a slight hill and turning to the left pretty hard. Then it seemed to be related to the power steering or so i thought. Anyway i finish and while cleaning off the deck at idle it stalls, it never stalls. I get on and try to start it....nothing. So i choke it and it fires, i quick get it into the garage and park it for the night. I have some thoughts but wouldn't mind some different points of view or if something like this has happened to someone. Thanks for listining. Here is a pic just cause i know how boring things get without pics 
But Paul, I have a peanut container over the fuel tank on the backhoe cap as the key lock leaks like a sieve....and a soup can over the exhaust, a washcloth over the stereo & gauges, and a beach towel over the cloth seat. I guess u could say i baby this thing 
Dave